LAJOS MOLNÁR PROFESSIONAL DATA

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LAJOS MOLN ´

AR – PROFESSIONAL DATA

September 27, 2015

Office Address: Department of Analysis, Bolyai Institute,

University of Szeged,

H-6720 Szeged, Aradi v´ertan´uk tere 1. Hungary

E-mail: [email protected]

URL: http://www.math.unideb.hu/˜molnarl/

Born: August 19, 1964; Kemecse, Hungary

Citizenship: Hungarian

Marital Status: Married, two daughters (born in 1994, 1997)

Degrees

MSc: Mathematics, University of Debrecen, 1988 (Antal J´arai, Adviser). Thesis: A class of measures equivalent to the Haar-measure, and stochastic processes on groups.

PhD: Mathematics, University of Debrecen, 1990. Thesis: HS opera-tor valued c.a.g.o.s. measures and reproducing kernel Hilbert A -modules.

DSc: Mathematics, Hungarian Academy of Sciences, 2005. Dissertation: Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces

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Employment

1988-1989: Assistant, Department of Mathematics, Teacher’s Training College, Ny´ıregyh´aza, Hungary.

1989-1993: Assistant, Institute of Mathematics and Informatics, University of Debrecen, Debrecen, Hungary.

1993-1996: Assistant Professor, Institute of Mathematics and Informatics, University of Debrecen, Debrecen, Hungary.

1996-2007: Associate Professor, Institute of Mathematics and Informatics, University of Debrecen, Debrecen, Hungary.

2007- : Full Professor, Institute of Mathematics, University of Debrecen, Debrecen, Hungary.

2010-2013: Head of Department of Analysis, Institute of Mathematics, Univer-sity of Debrecen, Debrecen, Hungary.

2012 Spring: Visiting Full Professor, Department of Mathematical Sciences, University of Memphis, Memphis, USA.

2015- : Full Professor, Bolyai Institute, University of Szeged, Szeged, Hun-gary.

2015- : Chair of Department of Analysis, University of Szeged, Szeged, Hungary.

Research Interest

In general: Functional Analysis, Operator Theory More specifically:

Operator algebras: isomorphisms, isometries, derivations, preservers, reflexivity.

Function algebras: isomorphisms, isometries.

Quantum structures: algebraic structures of operators in quantum mechanics and their transform-ations.

Inner product structures: H∗-algebras, Hilbert modules.

Visiting Researcher for Longer Period

1996: March-May, University of Maribor, Maribor, Slovenia, Scholarship of Soros Foundation.

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1996: October-December, University of Maribor, Maribor, Slovenia, Hun-garian State E¨otv¨os Scholarship.

1997: March-August, University of Paderborn, Paderborn, Germany, Schol-arship of the Konferenz der Deutschen Akademien der Wis-senschaften.

2002: July-June, 2003, University of Dresden, Dresden, Germany, Re-search Fellowship of Alexander von Humboldt Foundation.

2008: June-August, University of Dresden, Dresden, Germany, Alexander von Humboldt Foundation.

2010: June-August, University of Dresden, Dresden, Germany, Alexander von Humboldt Foundation.

2011: June-September, University of Ljubljana, Ljubljana, Slovenia, Re-search grant by the Slovenian ReRe-search Agency (ARRS) for renowned researchers from abroad.

2012: January-May, University of Memphis, Visiting Full Professor. 2013: September (1 month), University of Calabria and Instituto Nazionale

di Fisica Nucleare (INFN), Cosenza, Italy.

2015: July (1 month), University of Calabria and Instituto Nazionale di Fisica Nucleare (INFN), Cosenza, Italy.

Host of Visiting Researcher for Longer Period

2004: February-April, Gregor Dolinar, University of Ljubljana.

Grants, Research Projects

1991-1994: Grant from the Hungarian Scientific Research Fund (OTKA), Grant No. 1652. Team member.

1995-1998: Grant from the Hungarian Scientific Research Fund (OTKA), Grant No. T–016846. Team member.

1996-1999: Grant from the Hungarian Scientific Research Fund (OTKA), Grant No. F–019322. Project leader.

1997-1999: Bilateral research project supported by the Hungarian and Slovene governments. Registration No. OMFB SLO-2/96. Project leader on the Hungarian side.

1997-1999: Grant from the Ministry of Education, Hungary. Registration No. FKFP 0304/1997. Project leader.

1999-2002: Grant from the Hungarian Scientific Research Fund (OTKA), Grant No. T030082. Team member.

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2000-2002: Grant from the Ministry of Education, Hungary. Registration No. FKFP 0349/2000. Project leader.

2001-2002: Bilateral research project supported by the Hungarian and Slovene governments. Registration No. SLO-3/00. Project leader on the Hungarian side.

2004-2007: Grant from the Hungarian Scientific Research Fund (OTKA), Grant No. T046203. Project leader.

2007-2009: Grant from the Hungarian Scientific Research Fund (OTKA), Grant No. NK68040. Team member.

2010-2014: Grant from the Hungarian Scientific Research Fund (OTKA), Grant No. K81166. Project leader.

2010-2014: Grant from the Hungarian Scientific Research Fund (OTKA), Grant No. NK81402. Team member.

2011: Grant by the Slovenian Research Agency (ARRS) for renowned researchers from abroad. Registration No. 1000-11-780001 2012-2013: Bilateral research project supported by the Hungarian and

Slovene governments. Registration No. T ´ET 10-1-2011-0617. Project leader on the Hungarian side.

2012-2017: ”Lend¨ulet” Research Grant by the Hungarian Academy of Sci-ences. Head of Research Group.

2015-2016: HAS-MOST Hungarian-Taiwanese bilateral research project. Project leader on the Hungarian side.

2015-2019: Grant from the Hungarian Scientific Research Fund (OTKA), Grant No. K115383. Project leader.

Awards, Decorations, Honours, Prizes

1992: Géza Grünwald Award of János Bolyai Mathematical Society, Hungary

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1996: Scholarship of the Konferenz der Deutschen Akademien der Wissenschaften.

1997: Sz´echenyi Professorship for the period 1998-2001, Ministry of Education, Hungary

1998: Award of the International Symposia on Functional Equations for outstanding contribution to the 36th Symposium, 36th ISFE, Brno, Czech Republic

1999: P´al Erd˝os Award of the Mathematical Section of the Hungarian Academy of Sciences

2002: Research Fellowship of Alexander von Humboldt Foundation for 2002-2003.

2002: Bolyai Scholarship for the period 2002-2005, Hungarian Acad-emy of Sciences, Hungary

2006: Bolyai-Plaquette, Hungarian Academy of Sciences

2008: ”Publication of the Year” gold medal in the category of Science and Technology, University of Debrecen

2011: Grant by the Slovenian Research Agency (ARRS) for renowned foreign researchers for a 3-months research stay

2011: Academy Prize of the Hungarian Academy of Sciences

2012: Winner of the Momentum (Lend¨ulet) Program of the Hungarian Academy of Sciences

2015: Decoration called ”Knight’s Cross of the Order of Merit of the Republic of Hungary” given by the President of Hungary.

Organizing Conferences

1999: Functional Analysis and Applications: Memorial Conference for B´ela Sz˝okefalvi-Nagy, August 2–August 6, 1999, Szeged, Hun-gary. Local organizer.

2003: Von Neumann Centennial Conference: Linear Operators and Foundations of Quantum Mechanics, Budapest, Hungary, 15-20 October, 15-2003. Member of the Organizing Committee. 2013: ”Lend¨ulet” FIFA’13 Workshop, University of Debrecen, April

26-27, 2013, Debrecen, Hungary. Main organizer.

2013: Numbers, Functions, Equations 2013, June 28-30, 2013, Visegr´ad, Hungary. Member of the Organizing Committee. 2014: Young Functional Analysts’ Meeting 2014, Institute of

Mathe-matics, April 11-13, 2014, Debrecen, Hungary. Main organizer. 2014: CIMPA Research School on ”Operator theory and the prin-ciples of quantum mechanics” University Moulay Ismail, 2014 September 8-17, Meknes, Morocco. Member of the Scientific Committee.

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Editorial Work

Editor of Acta Math. Acad. Paedagog. Nyhaziensis. N.S. Editor of Journal of Linear and Topological Algebra Editor of Journal of Mathematical Analysis

Editor of Linear and Multilinear Algebra Editor of Mathematica Slovaca

Editor of Operators and Matrices

Editor of Periodica Mathematica Hungarica Editor of Publicationes Mathematicae (Debrecen)

Previously: Editor of Versita de Gruyter Book Publishing Pro-gram in Mathematics

Other Scientific Activities

2006-2009: Member of the Mathematical Jury of the Hungarian Scientific Research Fund

2007-2012: Member of the Doctoral Committee of the Section of Mathe-matics, Hungarian Academy of Sciences

2008-2011: Chairman of the Committee of Mathematics and Physics, De-brecen Branch of the Hungarian Academy of Sciences

2009-2011: Member of the Collegium ”Natural Sciences and Technology” of the Hungarian Scientific Research Fund

2010-2014: Councillor of the International Quantum Structure Association 2011-2014: Member of the Mathematical Committee of the Section of

Mathematics, Hungarian Academy of Sciences

2013-: Member of the Advisory Board of J´anos Bolyai Research Fel-lowship, Hungarian Academy of Sciences

2014-: Member of the Doctoral Committee of the Faculty of Science and Informatics, University of Szeged

2014-: Member of the Doctoral Council of the Hungarian Academy of Sciences

Membership in Societies

1989-: Member of J´anos Bolyai Mathematical Society. 1994-: Member of the American Mathematical Society.

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2013-: Member of the International Linear Algebra Society.

University Activities

1995-1996: Scientific advisor of the Library of the Institute of Mathematics and Informatics, University of Debrecen.

1995-1997: Member of the Mathematical Committee of the Institute of Mathematics and Informatics, University of Debrecen.

2005-2007: Vice-director of the Institute of Mathematics, University of De-brecen.

2008-2011: Member of the Scientific and Habilitation Council of the Faculty of Science and Technology, University of Debrecen.

2008-2015: Leader of the program ”Functional Analysis” in the Doctoral School ”Mathematics and Computer Sciences”, University of Debrecen.

Teaching Activities

University of Debrecen:

For undergraduates: Linear Algebra, Analysis I, II, III, Dif-ferential Equations, Real Variables, Measure and Integration, Complex Variables.

Mathematics 3 (in English) for foreign students of physics and electrical engineering, College Math - Functions (in English) for foreign students.

For graduates and PhD students: Functional Analysis, Ba-nach Algebras,C∗-algebras, von Neumann Algebras.

Budapest University of Technology and Economics:

Selected Topics in Functional Analysis, graduate course in 2014.

Teaching Activities Abroad

1996: Wintersemester, University of Maribor, Slovenia. Graduate Course in Real Analysis.

1997: Summersemester, University of Paderborn, Germany. Seminar Funktionentheorie/Zahlentheorie.

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2012: Springsemester, University of Memphis, Undergraduate Course on Linear Algebra.

2015: Special courses, Niigata University, Niigata, Japan. Undergrad-uate course on Functional Analysis. GradUndergrad-uate course on Pre-server Problems.

Lecture Notes

[1] Complex Functions, manuscript, in Hungarian, 1992.

[2] Spectral Theory and von Neumann Algebras, manuscript, in Hungarian, 1994.

[3] Banach Algebras, C∗-Algebras and von Neumann Algebras,

manuscript, in Hungarian, 2001.

Thesis Directed

1993: N´ora Kontra: Riesz representation theorems. (in Hungarian) [MSc]

1995: P´eter Batty´anyi: Jordan *-derivations on operator algebras. (in Hungarian) [Competition work, distinguished national first prize]

1996: P´eter Batty´anyi: Jordan *-derivations on operator algebras. (in Hungarian) [MSc]

1996: Tibor Moln´ar: Calculus in the secondary school. (in Hungarian) [MSc]

1997: Csaba Nosz´aly: Isomorphisms of function algebras. (in Hun-garian) [MSc]

1997: M´at´e Gy˝ory: Isometries of function algebras and semigroup isomorphisms of operator ideals. (in Hungarian) [Competition work, national first prize]

1998: Anna N´emeth: The three fundamental theorems of functional analysis. (in Hungarian) [MSc]

1998: M´at´e Gy˝ory: Isometries of function algebras and semigroup isomorphisms of operator ideals. (in Hungarian) [MSc]

1998: Zsolt Vida: Derivations, Jordan *-derivations and automor-phisms. (in Hungarian) [MSc]

1999: M´at´e Gy˝ory: Diameter preserving linear bijection ofC0(X) and the reflexivity of the isometry group of the suspension ofB(H). (in Hungarian) [Competition work, national first prize; ‘Pro Sci-entia Medal’ of the Hungarian Academy of Sciences]

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2001: Mátyás Barczy and Mariann Tóth: Local automorphisms of the sets of states and effects on a Hilbert space. (in Hungarian) [Competition work, national first prize]

2001: Mariann T´oth: Local maps of operator algebras. (in Hungarian) [MSc]

2008: Emese T¨unde Rozs´alyi: The life and work of Frigyes Riesz (in Hungarian) [MSc]

2010: Patr´ıcia Szokol: Classical and quantum relative entropy [MSc] 2011: Patr´ıcia Szokol: Maps on positive semidefinite operators

pre-serving relative entropy. [Competition work, national special prize]

PhD Students

– M´at´e Gy˝ory; (1998–2001) ’Preserver problems and reflexivity problems on operator algebras and on function algebras’, PhD Dissertation, 2003.

– Gerg˝o Nagy; (2008–2011) ’Preserver problems on structures of positive operators’, PhD Dissertation, 2013.

– Patr´ıcia Szokol; (2010–2013) ’Preserver problems and separa-tion theorems’, PhD Dissertasepara-tion, 2015.

– Roberto Beneduci; (2013–2014) ’Mathematical structures of positive operator valued measures and applications’, PhD Dis-sertation, 2014.

Membership in PhD Committees

— Vilmos Prokaj, Eötvös Loránd University, Budapest, April 9, 1999.

— Károly Nagy, University of Debrecen, Debrecen, May 31, 2001. — Bálint Farkas, Eötvös Loránd University, Budapest, May 26,

2004.

— Zsolt Balogh, University of Debrecen, Debrecen, September 21, 2004.

— Attila H´azy, University of Debrecen, Debrecen, October 7, 2005. — Zolt´an Kaiser, University of Debrecen, Debrecen, January 27,

2006.

— Fülöp Ágnes, Eötvös Loránd University, Budapest, May 5, 2006.

— Tibor Juh´asz, University of Debrecen, Debrecen, October 19, 2006.

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— P´eter Varga, University of Debrecen, Debrecen, December 21, 2006.

— ´Agnes Baran, University of Debrecen, Debrecen, November 27, 2007.

— Pál Burai, University of Debrecen, Debrecen, January 15, 2008. — Árpád Baricz, University of Debrecen, Debrecen, October 2,

2008.

— Izabella Stuhl, University of Debrecen, Debrecen, March 5, 2009.

— Endre Iglói, University of Debrecen, Debrecen, March 20, 2009. — Zoltán Léka, University of Szeged, Szeged, May 6, 2009. — Zita Makó, University of Debrecen, Debrecen, November 13,

2009.

— Fruzsina M´esz´aros, University of Debrecen, Debrecen, March 17, 2010.

— Andr´as Bazs´o, University of Debrecen, Debrecen, October 15, 2010.

— Istv´an Vajda, University of Debrecen, Debrecen, October 27, 2010.

— J´ozsef Kor´andi, University of Debrecen, Debrecen, June 12, 2012.

— ´Agota Orosz-Kaiser, University of Debrecen, Debrecen, June 27, 2012.

— Szabolcs Baják, University of Debrecen, Debrecen, July 3, 2012. — Zsolt Sz˝ucs, Eötvös Loránd University, Budapest, 2014.

— András Szántó, Budapest University of Technology and Eco-nomics, Budapest, January 23, 2015.

— Ferenc V´arady, University of Debrecen, Debrecen, February 11, 2015.

Membership in Habilitation Committees

— K´alm´an Liptai, University of Debrecen, Debrecen, November 24, 2011.

— Mih´aly Bessenyei, University of Debrecen, Debrecen, November 25, 2011.

— István Blahota, University of Debrecen, Debrecen, October 16, 2013. — Pál Burai, University of Debrecen, Debrecen, November 20, 2014. — Gábor Pusztai, University of Szeged, Szeged, October 9, 2015.

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— G´abor Elek, Hungarian Academy of Sciences, Budapest, Janu-ary 28, 2010.

— Tam´as Keleti, Hungarian Academy of Sciences, Budapest, De-cember 20, 2010.

— Alice Fialowski, Hungarian Academy of Sciences, Budapest, No-vember 14, 2011.

— S´andor Fridli, Hungarian Academy of Sciences, Budapest, May 11, 2015.

— M´at´e Matolcsi, Hungarian Academy of Sciences, Budapest, June 23, 2015.

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LIST OF PUBLICATIONS

Book

[MB] L. Moln´ar,Selected Preserver Problems on Algebraic Struc-tures of Linear Operators and on Function Spaces, Lecture Notes in Mathematics, Vol. 1895, p. 236, Springer, 2007. MR 2007g:47056, Zbl. 1119.47001

Research papers

[1] L. Moln´ar, J. Pitrik and D. Virosztek,Maps on positive def-inite matrices preserving Bregman and Jensen divergences,

preprint

[2] O. Hatori and L. Moln´ar,Generalized isometries of the spe-cial unitary group,preprint.

[3] O. Hatori and L. Moln´ar, Spectral conditions for Jordan *-isomorphisms on operator algebras, preprint.

[4] F. Botelho, L. Moln´ar and G. Nagy, Linear bijections on von Neumann factors commuting withλ-Aluthge transform,

submitted.

[5] L. Moln´ar and D. Virosztek, Continuous Jordan triple en-domorphisms of P2,submitted.

[6] L. Moln´ar and G. Nagy, Spectral order automorphisms on Hilbert space effects and observables: the 2-dimensional case, submitted.

[7] L. Moln´ar and P. Szokol,Transformations preserving norms of means of positive operators and nonnegative functions,

Integral Equations Operator Theory, to appear.

[8] L. Molnár Two characterizations of unitary-antiunitary similarity transformations of positive definite operators on a finite dimensional Hilbert space, Annales Univ. Sci. Bu-dapest., Sect. Comp. (special issue dedicated to Prof. Zoltán Sebestyén on the occasion of his 70th birthday), to appear. [9] L. Molnár, General Mazur-Ulam type theorems and some applications, in Operator Semigroups Meet Complex Anal-ysis, Harmonic Analysis and Mathematical Physics, W.

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Arendt, R. Chill, Y. Tomilov (Eds.), Operator Theory: Ad-vances and Applications, Vol. 250, to appear.

[10] L. Moln´ar and D. Virosztek, On algebraic endomorphisms of the Einstein gyrogroup,J. Math. Phys.56(2015), 082302. [11] L. Moln´ar On the nonexistence of order isomorphisms be-tween the sets of all self-adjoint and all positive definite operators, Abstr. Appl. Anal. Volume 2015 (2015), Article ID 434020, 6 pages.

IF: 1,274**

[12] L. Moln´ar, P. ˇSemrl and A.R. Sourour, Bilocal automor-phisms, Oper. Matrices 9 (2015), 113–120.

IF: 0,529**

[13] L. Moln´ar and P. Szokol,Transformations on positive defi-nite matrices preserving generalized distance measures, Lin-ear Algebra Appl. 466 (2015), 141–159.

IF: 0,983**

[14] L. Moln´ar,Jordan triple endomorphisms and isometries of spaces of positive definite matrices, Linear Multilinear Alg. 63 (2015), 12–33.

IF: 0,700**

[15] L. Moln´ar and G. Nagy, Transformations on density oper-ators that leave the Holevo bound invariant, Int. J. Theor. Phys. 53 (2014), 3273–3278.

IF: 1,188**

[16] R. Beneduci and L. Moln´ar,On the standard K-loop struc-ture of positive invertible elements in aC∗-algebra, J. Math. Anal. Appl. 420(2014), 551–562.

IF: 1,119**

[17] L. Moln´ar,A few conditions for a C∗-algebra to be commu-tative, Abstr. Appl. Anal. Volume 2014 (2014), Article ID 705836, 4 pages.

IF: 1,274**

[18] L. Moln´ar and P. Szokol,Kolmogorov-Smirnov isometries of the space of generalized distribution functions, Math. Slo-vaca 64 (2014), 433–444.

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[19] L. Moln´ar, Bilocal *-automorphisms ofB(H),Arch. Math. 102 (2014), 83–89.

IF: 0,479**

[20] O. Hatori and L. Moln´ar, Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in C∗-algebras, J. Math. Anal. Appl.409 (2014), 158–167.

IF: 1,119**

[21] L. Moln´ar,Jordan triple endomorphisms and isometries of unitary groups, Linear Algebra Appl. 439 (2013), 3518– 3531.

IF: 0,983

[22] F. Botelho, J. Jamison and L. Moln´ar,Surjective isometries on Grassmann spaces, J. Funct. Anal. 265 (2013), 2226– 2238.

IF: 1,152

[23] F. Botelho, J. Jamison and L. Moln´ar, Algebraic reflexivity of isometry groups and automorphism groups of some oper-ator structures,J. Math. Anal. Appl.408 (2013), 177–195. IF: 1,119

[24] L. Moln´ar, G. Nagy and P. Szokol, Maps on density opera-tors preserving quantum f-divergences,Quantum Inf. Pro-cess. 12(2013), 2309–2323.

IF: 2,960

[25] G. Dolinar and L. Moln´ar,Automorphisms for the logarith-mic product of positive semidefinite operators, Linear Mul-tilinear Algebra 61 (2013), 161–169.

IF: 0,700

[26] O. Hatori, G. Hirasawa, T. Miura and L. Moln´ar,Isometries and maps compatible with inverted Jordan triple products on groups, Tokyo J. Math.35(2012), 385–410.

IF: 0,258

[27] O. Hatori and L. Moln´ar, Isometries of the unitary group, Proc. Amer. Math. Soc. 140 (2012), 2141–2154. MR2888199, Zbl. 1244.47032

IF: 0,609

[28] G. Dolinar and L. Moln´ar, Sequential endomorphisms of finite dimensional Hilbert space effect algebras, J. Phys. A: Math. Theor. 45 (2012) 065207. MR2881058, Zbl.

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1235.81008 IF: 1,766

[29] L. Moln´ar and P. ˇSemrl, Transformations of the unitary group on a Hilbert space, J. Math. Anal. Appl.388(2012), 1205–1217. MR2869819, Zbl. 06009629

IF: 1,050

[30] L. Moln´ar and G. Nagy, Isometries and relative entropy preserving maps on density operators, Linear Multilinear Algebra 60(2012), 93–108. MR2869675, Zbl 1241.47034 IF: 0,677

[31] L. Moln´ar, Maps preserving general means of positive op-erators, Electron. J. Linear Algebra 22 (2011), 864–874. MR2836790, Zbl. 06098828

IF: 0,563

[32] L. Moln´ar,Continuous maps on matrices transforming geo-metric mean to arithmetic mean, Annales Univ. Sci. Bu-dapest., Sect. Comp. (special issue dedicated to Prof. Antal J´arai on the occasion of his 60th birthday)35(2011), 217– 222. MR?? Zbl. 1229.47055

[33] L. Moln´ar and W. Timmermann, Transformations on bounded observables preserving measure of compatibility,

Int. J. Theor. Phys.50(2011), 3857–3863. MR2860043, Zbl. 1243.81079

IF: 0,845

[34] L. Moln´ar, Kolmogorov-Smirnov isometries and affine au-tomorphisms of spaces of distribution functions,Cent. Eur. J. Math. 9(2011), 789–796. MR2805312, Zbl. 1239.46022 IF: 0,440

[35] L. Moln´ar,L´evy isometries of the space of probability distri-bution functions,J. Math. Anal. Appl.380(2011), 847–852. MR2794437, Zbl. 1229.46019

IF: 1,001

[36] L. Moln´ar, Order automorphisms on positive definite op-erators and a few applications, Linear Algebra Appl. 434 (2011), 2158–2169. MR2781684, Zbl. 1220.47051

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[37] L. Moln´ar and P. Szokol, Maps on states preserving the relative entropy II,Linear Algebra Appl.432(2010), 3343– 3350. MR 2011b:47087, Zbl. 1187.47030

IF: 1,005

[38] L. Moln´ar and G. Nagy, Thompson isometries on positive operators: the2-dimensional case,Electron. J. Lin. Alg.20 (2010), 79–89. MR2596446, Zbl. 1195.46017

IF: 0,808

[39] L. Moln´ar, Linear maps on observables in von Neumann algebras preserving the maximal deviation,J. London Math. Soc.81(2010), 161–174. MR 2010m:46100, Zbl. 1189.47036 IF: 0,828

[40] L. Moln´ar, Thompson isometries of the space of invert-ible positive operators, Proc. Amer. Math. Soc.137(2009), 3849–3859. MR 2010h:47058, Zbl. 1184.46021

IF: 0,64

[41] L. Moln´ar,Maps preserving the harmonic mean or the par-allel sum of positive operators, Linear Algebra Appl. 430 (2009), 3058–3065. MR 2010e:47077, Zbl. 1182.47035 IF: 1,073

[42] L. Moln´ar, Maps on positive operators preserving Lebesgue decompositions,Electron. J. Linear Algebra18(2009), 222– 232. MR 2010i:47079, Zbl. 1181.47040

IF: 0,892

[43] L. Moln´ar and W. Timmermann, A metric on the space of projections admitting nice isometries, Studia Math.191 (2009), 271–281. MR 2009m:47097, Zbl. 1168.47030

IF: 0,645

[44] L. Moln´ar, Maps preserving the geometric mean of positive operators, Proc. Amer. Math. Soc.137 (2009), 1763–1770. MR 2009m:47096, Zbl. 1183.47032

IF: 0,64

[45] L. Moln´ar and W. Timmermann,Maps on quantum states preserving the Jensen-Shannon divergence, J. Phys. A: Math. Theor. 42 (2009), 015301. MR 2010f:81033, Zbl. 1156.81349

IF: 1,577

[46] L. Moln´ar, Linear maps on matrices preserving commuta-tivity up to a factor,Linear Multilinear Algebra57(2009),

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13–18. MR 2010i:15003, Zbl. 1160.15004 IF: 0,74

[47] G. Dolinar and L. Moln´ar, Isometries of the space of dis-tribution functions with respect to the Kolmogorov-Smirnov metric, J. Math. Anal. Appl., 348 (2008), 494–498. MR 2009j:47063, Zbl. 1162.46305

IF: 1,046

[48] L. Moln´ar, Maps on the n-dimensional subspaces of a Hilbert space preserving principal angles, Proc. Amer. Math. Soc. 136 (2008), 3205–3209. MR 2009f:47056, Zbl. 1143.47025

IF: 0,584

[49] L. Moln´ar, Maps on states preserving the relative entropy,

J. Math. Phys. 49 (2008), 032114. MR 2009c:81025, Zbl. 1153.81407

IF: 1,085

[50] L. Moln´ar, Isometries of the spaces of bounded frame func-tions, J. Math. Anal. Appl. 338 (2008), 710–715. MR 2009d:47038, Zbl. 1135.47034

IF: 1,046

[51] G. Dolinar and L. Moln´ar, Maps on quantum observables preserving the Gudder order, Rep. Math. Phys. 60 (2007), 159–166. MR 2008m:81008, Zbl. 1131.81010

IF: 0,624

[52] L. Moln´ar and P. ˇSemrl, Spectral order automorphisms of the spaces of Hilbert space effects and observables, Lett. Math. Phys. 80 (2007), 239–255. MR 2008f:47118, Zbl. 1138.47057

IF: 1,044

[53] L. Moln´ar and W. Timmermann, Mixture preserving maps on von Neumann algebra effects, Lett. Math. Phys. 79 (2007), 295–302. MR 2008b:46084, Zbl. 1130.46037

IF: 1,044

[54] L. Moln´ar and P. ˇSemrl, Elementary operators on self-adjoint operators, J. Math. Anal. Appl. 327 (2007), 302– 309. MR 2007g:47052, Zbl. 1117.47024

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[55] L. Moln´ar,Multiplicative Jordan triple isomorphisms on the self-adjoint elements of von Neumann algebras, Linear Al-gebra Appl. 419 (2006), 586–600. MR 2007k:47059, Zbl. 1115.47034

IF: 0,585

[56] L. Moln´ar, Non-linear Jordan triple automorphisms of sets of self-adjoint matrices and operators, Studia Math. 173 (2006), 39–48. MR 2006j:47059, Zbl. 1236.47031

IF: 0,515

[57] L. Moln´ar and W. Timmermann, Transformations on the sets of states and density operators, Linear Algebra Appl. 418 (2006), 75–84. MR 2007g:81014, Zbl. 1113.47023 IF: 0,585

[58] L. Moln´ar, A remark to the Kochen-Specker theorem and some characterizations of the determinant on sets of Her-mitian matrices,Proc. Amer. Math. Soc.134(2006) 2839– 2848. MR 2007b:81018, Zbl. 1094.15010

IF: 0,513

[59] L. Moln´ar and P. ˇSemrl, Non-linear commutativity pre-serving maps on self-adjoint operators, Quart. J. Math.56 (2005), 589–595. MR 2006m:47063, Zbl. 1211.47075

IF: 0,868

[60] E. Kov´acs and L. Moln´ar,Preserving some numerical corre-spondences between Hilbert space effects, Rep. Math. Phys. 54 (2004), 201–209. MR 2005m:47077, Zbl. 1100.47032 IF: 0,625

[MDiss] L. Moln´ar, Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces, Dissertation for the D.Sc. degree of the Hungarian Academy of Sciences, 241 pages.

[61] L. Moln´ar, Sequential isomorphisms between the sets of von Neumann algebra effects, Acta Sci. Math. (Szeged) 69 (2003), 755–772. MR 2005d:46128, Zbl. 1049.46048

[62] L. Moln´ar and E. Kov´acs, An extension of a characteriza-tion of the automorphisms of Hilbert space effect algebras,

Rep. Math. Phys.52(2003), 141–149. MR 2004i:81015, Zbl. 1052.81007

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[63] L. Moln´ar and M. Barczy, Linear maps on the space of all bounded observables preserving maximal deviation, J. Funct. Anal. 205 (2003), 380–400. MR 2004j:47074, Zbl. 1047.47029

IF: 0,993

[64] L. Moln´ar, Preservers on Hilbert space effects, Linear Al-gebra Appl. 370 (2003), 287–300. MR 2004g:81022, Zbl. 1040.47028

IF: 0,656

[65] L. Moln´ar and W. Timmermann, Preserving the measure of compatibility between quantum states,J. Math. Phys.44 (2003), 969–973. MR 2004:81010, Zbl. 1061.81001

IF: 1,481

[66] L. Moln´ar and W. Timmermann, Isometries of quantum states, J. Phys. A: Math. Gen. 36 (2003), 267–273. MR 2004a:81046, Zbl. 1047.81017

IF: 1,357

[67] L. Moln´ar, Local automorphisms of operator algebras on Banach spaces, Proc. Amer. Math. Soc. 131(2003), 1867– 1874. MR 2003j:47050, Zbl. 1043.47030

IF: 0,389

[68] L. Moln´ar and P. ˇSemrl, Elementary operators on stan-dard operator algebras, Linear and Multilinear Algebra 50 (2002), 315–319. MR 2003g:47067, Zbl. 1033.47026

IF: 0,353

[69] L. Moln´ar,Orthogonality preserving transformations on in-definite inner product spaces: generalization of Uhlhorn’s version of Wigner’s theorem, J. Funct. Anal., 194 (2002), 248–262. MR 2003h:47069, Zbl. 1010.46023

IF: 0,924

[70] F. Cabello S´anchez and L. Moln´ar, Reflexivity of the isom-etry group of some classical spaces,Rev. Mat. Iberoam.18 (2002), 409–430. MR 2003j:47046, Zbl. 1050.47028

IF: 0,525

[71] L. Moln´ar, 2-local isometries of some operator alge-bras, Proc. Edinb. Math. Soc. 45 (2002), 349–352. MR 2003e:47067, Zbl. 1027.46062

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[72] L. Moln´ar, Conditionally multiplicative maps on the set of all bounded observables preserving compatibility, Linear Al-gebra Appl. 349 (2002), 197–201. MR 2003c:47070, Zbl. 998.81002

IF: 0,462

[73] L. Moln´ar, On certain automorphisms of sets of partial isometries,Arch. Math.78(2002), 43–50. MR 2002k:47078, Zbl. 1037.47025

IF: 0,326

[74] L. Moln´ar,Some characterizations of the automorphisms of B(H) andC(X),Proc. Amer. Math. Soc.130(2002), 111-120. MR 2002m:47047, Zbl. 983.47024

IF: 0,334

[75] L. Moln´ar, Jordan maps on standard operator algebras,

Functional Equations – Results and Advances, in Z. Dar´oczy and Zs. P´ales (eds.), Advances in Mathematics, vol 3., Kluwer Acad. Publ., Dordrecht, 2001, pp. 305–320. MR 2003e:47068, Zbl. 1004.46044

[76] L. Moln´ar, On some functional equations on operator al-gebras, in Hungarian, Assembly Lectures, May 2000, vol. II, Hungarian Academy of Sciences, Budapest, 2001, pp. 457–464.

[77] L. Moln´ar,Local automorphisms of some quantum mechan-ical structures, Lett. Math. Phys. 58 (2001), 91–100. MR 2002k:47077, Zbl. 1002.46044

IF: 0,819

[78] L. Moln´ar, Fidelity preserving maps on density operators, Rep. Math. Phys. 48 (2001), 299–303. MR 2003a:81081, Zbl. 1002.46044

IF: 0,475

[79] L. Moln´ar, Order-automorphisms of the set of bounded observables, J. Math. Phys. 42 (2001), 5904–5909. MR 2002m:81012, Zbl. 1019.81005

IF: 1,151

[80] L. Moln´ar, *-semigroup endomorphisms of B(H), in I. Gohberg et al. (Edt.), Operator Theory: Advances and Applications, Vol. 127, pp. 465–472, Birkh¨auser, 2001. MR1902817, Zbl. 991.47019

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[81] L. Moln´ar, Characterizations of the automorphisms of Hilbert space effect algebras, Commun. Math. Phys. 223 (2001), 437–450. MR 2003a:81013, Zbl. 1029.81008

IF: 1,729

[82] L. Moln´ar and Zs. P´ales, ⊥-order automorphisms of Hilbert space effect algebras: The two-dimensional case, J. Math. Phys. 42 (2001), 1907–1912. MR 2001m:47141, Zbl. 1025.47045

IF: 1,151

[83] L. Moln´ar,Transformations on the set of alln-dimensional subspaces of a Hilbert space preserving principal an-gles, Commun. Math. Phys. 217 (2001), 409–421. MR 2002b:81008, Zbl. 1026.81006

IF: 1,729

[84] L. Moln´ar, A reflexivity problem concerning the C∗-algebra C(X)⊗B(H), Proc. Amer. Math. Soc. 129 (2001), 531– 537. MR 2001e:46101, Zbl. 959.47022

IF: 0,369

[85] L. Moln´ar, A Wigner-type theorem on symmetry trans-formations in Banach spaces, Publ. Math. (Debrecen) 58 (2000), 231–239. MR 2001j:47092, Zbl. 973.47058

IF: 0,171

[86] M. Breˇsar, L. Moln´ar and P. ˇSemrl, Elementary opera-tors II, Acta Sci. Math. (Szeged)66 (2000), 769–791. MR 2002h:47053, Zbl. 973.47028

[87] L. Moln´ar,On isomorphisms of standard operator algebras,

Studia Math. 142 (2000), 295–302. MR 2001g:47124, Zbl. 1049.47503

IF: 0,477

[88] L. Moln´ar, A Wigner-type theorem on symmetry transfor-mations in type II factors, Int. J. Theor. Phys. 39 (2000), 1463–1466. MR 2001i:46098, Zbl. 1090.46510

IF: 0,598

[89] L. Moln´ar, On some automorphisms of the set of effects on Hilbert space, Lett. Math. Phys. 51(2000), 37–45. MR 2001g:81109, Zbl. 1072.81535

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[90] L. Moln´ar and P. ˇSemrl,Local automorphisms of the unitary group and the general linear group on a Hilbert space, Expo. Math.18(2000), 231–238. MR 2001a:47083, Zbl. 963.46044 [91] L. Moln´ar, Generalization of Wigner’s unitary-antiunitary theorem for indefinite inner product spaces, Commun. Math. Phys. 210 (2000), 785–791. MR 2001g:47064, Zbl. 957.46106

IF: 1,721

[92] L. Moln´ar, Reflexivity of the automorphism and isome-try groups of C∗-algebras in BDF theory, Arch. Math. 74 (2000), 120–128. MR 2001k:47049, Zbl. 1023.47021

IF: 0,305

[93] L. Moln´ar, Automatic surjectivity of ring homomorphisms onH∗-algebras and algebraic differences among some group algebras of compact groups, Proc. Amer. Math. Soc. 128 (2000), 125–134. MR 2000c:46103, Zbl. 945.46034

IF: 0,394

[94] L. Moln´ar and B. Zalar, On local automorphism of group algebras of compact groups, Proc. Amer. Math. Soc. 128 (2000), 93–99. MR 2000f:43002, Zbl. 930.43002

IF: 0,394

[95] L. Moln´ar,Multiplicative maps on ideals of operators which are local automorphisms, Acta Sci. Math. (Szeged) 65 (1999), 727–736. MR 2000k:47045, Zbl. 993.47031

[96] L. Moln´ar, Some multiplicative preservers on B(H), Lin-ear Algebra Appl. 301(1999), 1–13. MR 2000h:47060, Zbl. 974.47031

IF: 0,385

[97] L. Moln´ar,A generalization of Wigner’s unitary-antiunitary theorem to Hilbert modules,J. Math. Phys.40(1999), 5544– 5554. MR 2000j:46112, Zbl. 953.46030

IF: 0,976

[98] L. Moln´ar and B. Zalar,Reflexivity of the group of surjective isometries on some Banach spaces, Proc. Edinb. Math. Soc. 42 (1999), 17–36. MR 2000b:47094, Zbl. 930.47015

IF: 0,225

[99] L. Moln´ar, Some linear preserver problems on B(H) con-cerning rank and corank, Linear Algebra Appl.286(1999),

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311-321. MR 2000b:47089, Zbl. 963.47028 IF: 0,385

[100] L. Moln´ar, An algebraic approach to Wigner’s unitary-antiunitary theorem, J. Austral. Math. Soc.65(1998), 354– 369. MR 99k:46031, Zbl. 943.46033

IF: 0,330

[101] L. Moln´ar and P. ˇSemrl,Some linear preserver problems on upper triangular matrices, Linear and Multilinear Algebra 45 (1998), 189–206. MR 99h:15003, Zbl. 974.15001

[102] V. Mascioni and L. Moln´ar, Linear maps on factors which preserve the extreme points of the unit ball, Canad. Math. Bull. 41 (1998), 434–441. MR 99m:46145, Zbl. 919.47024 IF: 0,265

[103] L. Moln´ar, The automorphism and isometry groups of `∞(N,B(H)) are topologically reflexive, Acta Sci. Math.

(Szeged)64(1998), 671–680. MR 99k:47083, Zbl. 937.47039 [104] L. Moln´ar and M. Gy˝ory, Reflexivity of the automor-phism and isometry groups of the suspension of B(H), J. Funct. Anal. 159 (1998), 568–586. MR 2000h:47110, Zbl. 933.46064

IF: 0,760

[105] M. Gy˝ory and L. Moln´ar, Diameter preserving linear bi-jections of C(X), Arch. Math. 71 (1998), 301–310. MR 99h:46098, Zbl. 928.46034

IF: 0,216

[106] M. Gy˝ory, L. Moln´ar and P. ˇSemrl,Linear rank and corank preserving maps onB(H)and an application to *-semigroup isomorphisms of operator ideals, Linear Algebra Appl.280 (1998), 253–266. MR 2000k:47044, Zbl. 940.46012

IF: 0,392

[107] L. Moln´ar, Stability of the surjectivity of Jordan *-homomorphisms of B(H), J. Nat. Geom. 14 (1998), 149– 154. MR 99g:46102, Zbl. 932.46040

[108] L. Moln´ar, Characterization of additive *-homomorphisms and Jordan *-homomorphisms on operator ideals, Aequa-tiones Math. 55 (1998), 259–272. MR: 99m:47042, Zbl. 912.47017

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[109] L. Moln´ar, A proper standard C∗-algebra whose automor-phism and isometry groups are topologically reflexive, Publ. Math. (Debrecen) 52(1998), 563–574. MR 99e:46082, Zbl. 918.46055

IF: 0,098

[110] L. Moln´ar, Stability of the surjectivity of endomorphisms and isometries of B(H), Proc. Amer. Math. Soc. 126 (1998), 853–861. MR 98e:47055, Zbl. 890.47022

IF: 0,363

[111] L. Moln´ar and P. ˇSemrl, Order isomorphisms and triple isomorphisms of operator ideals and their reflexivity, Arch. Math. 69(1997), 497–506. MR 99a:47054, Zbl. 910.47027 IF: 0,281

[112] L. Moln´ar, Jordan *-derivation pairs on a complex *-algebra, Aequationes Math. 54 (1997), 44–55. MR 98j:46053, Zbl. 887.16021

[113] L. Moln´ar and B. Zalar,Three-variable *-identities and ho-momorphisms of Schatten classes, Publ. Math. (Debrecen) 50 (1997), 121–133. MR 98h:46054, Zbl. 880.46042

IF: 0,089

[114] L. Moln´ar, The set of automorphisms of B(H) is topologi-cally reflexive in B(B(H)), Studia Math.122 (1997), 183– 193. MR 98e:47068, Zbl. 871.47030

IF: 0,452

[115] L. Moln´ar and P. ˇSemrl,Local Jordan *-derivations of stan-dard operator algebras, Proc. Amer. Math. Soc.125(1997), 447–454. MR 97d:47038, Zbl. 861.47020

IF: 0,273

[116] L. Moln´ar, On rings of differentiable functions, Grazer Math. Ber. 327 (1996), 13–16. MR 98e:46035, Zbl. 887.46009

[117] L. Moln´ar,Bijectivity of *-endomorphisms ofB(H) and the unilateral shift, Monatsh. Math. 122 (1996), 377–387. MR 97m:47047, Zbl. 862.46032

IF: 0,299

[118] C.J.K. Batty and L. Moln´ar, On topological reflexivity of the groups of *-automorphisms and surjective isometries of

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866.47027 IF: 0,170

[119] L. Moln´ar, The range of a Jordan *-derivation, Math. Japon. 44(1996), 353–356. MR 97m:47046, Zbl. 886.47019 [120] L. Moln´ar, The range of a Jordan *-derivation on an H∗-algebra, Acta Math. Hung. 72 (1996), 261–267. MR 98g:46078, Zbl. 902.46027

IF: 0,139

[121] L. Moln´ar, Wigner’s unitary-antiunitary theorem via Her-stein’s theorem on Jordan homomorphisms, J. Nat. Geom. 10 (1996), 137–148. MR 97i:46038, Zbl. 858.46019

[122] L. Moln´ar, Two characterizations of additive *-automorphisms of B(H), Bull. Austral. Math. Soc. 53 (1996), 391–400. MR 97c:47042, Zbl. 879.46030

IF: 0,163

[123] L. Moln´ar,The range of a ring homomorphism from a com-mutative C∗-algebra, Proc. Amer. Math. Soc. 124 (1996), 1789–1794. MR 96h:46090, Zbl. 857.46032

IF: 0,300

[124] L. Moln´ar, Locally inner derivations of standard operator algebras, Math. Bohem. 121 (1996), 1–7. MR 97i:47069, Zbl. 863.46039

[125] L. Moln´ar,Algebraic difference between p-classes of an H*-algebra, Proc. Amer. Math. Soc. 124 (1996), 169-175. MR 96d:46072, Zbl. 840.46035

IF: 0,300

[126] L. Moln´ar, A condition for a subspace of B(H) to be an ideal, Linear Algebra Appl. 235 (1996), 229–234. MR 96m:47092, Zbl. 852.46021

IF: 0,341

[127] L. Moln´ar and B. Zalar,On automatic surjectivity of Jordan homomorphisms,Acta Sci. Math. (Szeged)61(1995), 413– 424. MR 97a:46097, Zbl. 842.46046

[128] L. Moln´ar, On centralizers of an H*-algebra, Publ. Math. (Debrecen)46(1995), 89–95. MR 96a:46102, Zbl. 860.46037 IF: 0,101

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[129] L. Moln´ar,Conditions for a function to be a centralizer on an H*-algebra, Acta Math. Hung. 67(1995), 171–174. MR 96b:46074, Zbl. 888.46037

IF: 0,145

[130] L. Moln´ar, On the range of a normal Jordan *-derivation,

Comment. Math. Univ. Carolinae 35(1994), 691–695. MR 95k:47054, Zbl. 821.47028

[131] L. Moln´ar,A condition for a function to be a bounded linear operator, Indian J. Math. 35 (1993), 1–4. MR 94k:47061, Zbl. 811.47032

[132] L. Moln´ar, p-classes of an H*-algebra and their represen-tations, Acta Sci. Math. (Szeged)58 (1993), 411–423. MR 95c:46081, Zbl. 811.46056

[133] L. Moln´ar, On A-linear operators on a Hilbert A-module,

Period. Math. Hung. 26 (1993), 219–222. MR 94i:46062, Zbl. 816.46042

[134] L. Moln´ar, On Saworotnow’s Hilbert A-modules, Glasnik Mat. 28(1993), 259–267. MR 95m:46076, Zbl. 818.46056 [135] L. Moln´ar, Modular bases in a Hilbert A-module, Czech.

Math. J.42(1992), 649–656. MR 93i:46095, Zbl. 809.46039 IF: 0,132

[136] L. Moln´ar, ∗-representations of the trace-class of an H∗ -algebra, Proc. Amer. Math. Soc.115 (1992), 167–170. MR 92i:46064, Zbl. 789.46044

IF: 0,263

[137] L. Moln´ar, A note on the strong Schwarz inequality in HilbertA-modules,Publ. Math. (Debrecen)40(1992), 323– 325. MR 93i:46094, Zbl. 804.46056

IF: 0,038

[138] L. Moln´ar,A note on Saworotnow’s representation theorem on positive definite functions, Houston J. Math.17(1991), 89–99. MR 92j:46097, Zbl. 780.46035

IF: 0,198

[139] L. Moln´ar, Reproducing kernel Hilbert A-modules, Glasnik Mat. 25(1990), 335–345. MR 94k:46103, Zbl. 773.46026

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[140] Y. Kakihara and L. Moln´ar,A remark on HS operator val-ued c.a.g.o.s. measures, Res. Act. Fac. Sci. Engrg. Tokyo Denki Univ. 12(1990), 13–19. MR 91h:46082

[141] L. Moln´ar,Two applications of the theory of weakly station-ary stochastic processes to harmonic analysis,Glasnik Mat. 25 (1990), 209–219. MR 92h:60055, Zbl. 825.60027

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LIST OF INDEPENDENT CITATIONS (without self- or co-authors’ citations)

ordered according to the cited work

[1] L. Moln´ar,Reproducing kernel HilbertA-modules,Glasnik Mat. 25(1990), 335–345.

I (1) B. Zalar, Theory of Hilbert triple systems, Yokohama

Math. J.41(1994), 94–126.

I(2) B. Zalar,Jordan - von Neumann theorem for Saworotnow’s generalized Hilbert space, Acta Math. Hung. 69 (1995), 301– 325.

I(3) B. Zalar, Connections between Hilbert triple systems and involutiveH∗-triples,Acta Sci. Math. (Szeged)62(1996), 127– 143.

[2] L. Moln´ar, A note on Saworotnow’s representation theorem on positive definite functions,Houston J. Math.17(1991), 89–99.

Math. J.41(1994), 94–126.

I(5) B. Zalar,Jordan - von Neumann theorem for Saworotnow’s generalized Hilbert space, Acta Math. Hung. 69 (1995), 301– 325.

[3] L. Moln´ar, A note on the strong Schwarz inequality in Hilbert A-modules, Publ. Math. (Debrecen) 40(1992), 323–325.

I(7) S. Banić, D. Iliˇsević and S. Varoˇsanec, Bessel and Grüss type inequalities in inner product modules, Proc. Edinburgh Math. Soc.50 (2007), 23–36.

I(8) A.G. Ghazanfari and S.S. DragomirBessel and Gr¨uss type inequalities in inner product modules over Banach *-algebras,

J. Inequal. Appl. Volume 2011, Article ID 562923, 16 pages.

I (9) D. Iliˇsevi´c, Moln´ar-dependence in a pre-Hilbert module over anH∗-algebra, Acta Math. Hungar. 101(2003), 69–78.

I(10) D. Iliˇsevi´c and S. Varoˇsanec, Gr¨uss type inequalities in inner product modules, Proc. Amer. Math. Soc. 133 (2005), 3271–3280.

I(11) T.W. Palmer, Banach Algebras and the General Theory of *-Algebras, vol. II.,Cambridge University Press, 2001.

I(12) B. Zalar, Jordan - von Neumann theorem for Saworot-now’s generalized Hilbert space, Acta Math. Hung. 69 (1995), 301–325.

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[4] L. Moln´ar,∗-representations of the trace-class of an H∗-algebra,

Proc. Amer. Math. Soc. 115(1992), 167–170.

Math. J.41(1994), 94–126.

[5] L. Moln´ar,Modular bases in a Hilbert A-module,Czech. Math. J.42 (1992), 649–656.

I(17) D. Bakiˇc and B. Guljaˇs,Operators on HilbertH∗-modules,

J. Operator Theory 46(2001), 123–141.

I (18) D. Bakiˇc and B. Guljaˇs, Hilbert C∗-modules over C∗ -algebras of compact operators, Acta Sci. Math. (Szeged) 68 (2002), 249–269.

[6] L. Moln´ar, On Saworotnow’s Hilbert A-modules, Glasnik Mat. 28(1993), 259–267.

[7] L. Moln´ar, On A-linear operators on a Hilbert A-module, Pe-riod. Math. Hung. 26(1993), 219–222.

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[8] L. Moln´ar,p-classes of an H*-algebra and their representations,

Acta Sci. Math. (Szeged)58 (1993), 411–423.

Math. J.41(1994), 94–126.

[9] L. Moln´ar,On the range of a normal Jordan *-derivation, Com-ment. Math. Univ. Carolinae 35(1994), 691–695.

I (27) P. Batty´anyi, On the range of a Jordan *-derivation,

Comment. Math. Univ. Carolinae37 (1996), 659–665.

I (28) P. Batty´anyi, Jordan *-derivations with respect to the Jordan-product,Publ. Math. (Debrecen) 48(1996), 327–338.

I(29) M.A. Chebotar, Y. Fong and P.H. Lee,On maps preserv-ing zeros of the polynomialxy−yx∗,Linear Algebra Appl.408 (2005), 230–243.

I (30) J. Cui and C. Park, Maps preserving strong skew Lie product on factor Von Neumann algebras,Acta Math. Sci. (Ser. B Engl. Ed.)32 (2012), 531–538.

I(31) A. Taghavi,When is a subspace ofB(X)ideal?,Southeast

Asian Bull. Math.26 (2002), 153–158.

[10] L. Moln´ar, Conditions for a function to be a centralizer on an H*-algebra,Acta Math. Hung. 67(1995), 171–174.

Math. J.41(1994), 94–126.

[11] L. Moln´ar,On centralizers of an H*-algebra, Publ. Math. (De-brecen)46(1995), 89–95.

I(33) S. Ali and N.A. Dar, On left centralizers of prime rings with involution, Palestine Journal of Mathematics 3 (2014), 505–511.

I(34) S. Ali and C. Haetinger,On Jordanα-centralizers in rings and some applications,Bol. Soc. Paran. Mat.26(2008), 71–80.

I (35) M. Ashraf and S. Ali, On (α, β)∗-derivations in H∗

-algebras, Adv. Algebra 2 (2009), 23–31.

I (36) M. Ashraf and M.R. Mozumder, On Jordan α∗ -centralizers in semiprime rings with involution, Int. J. Con-temp. Math. Sciences 7(2012), 1103–1112.

I(37) M. Ashraf, N. Rehman, S. Ali and M.R. Mozumder, On generalized (θ, φ)-derivations in semiprime rings with involu-tion,Math. Slovaca 62(2012), 451–460.

I (38) M.J. Atteya, On generalized derivations of semiprime rings, Int. J. Algebra4 (2010), 591–598.

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I(39) M.J. Atteya,A note on generalized Jordan derivations in semiprime rings,Mathematics and Statistics 3 (2015), 7–9.

I(40) M.J. Atteya and D.I. Resan, Commuting derivations of semiprime rings, Int. J. Contemp. Math. Sciences 6 (2011), 1151–1158.

I(41) D. Benkoviˇc and D. Eremita, Characterizing left central-izers by their action on a polynomial, Publ. Math. (Debrecen) 64(2004), 343–351.

I(42) M.N. Daif and M.S. Tammam El-Sayiad,An identity re-lated to generalized derivations, Internat. J. Algebra 1 (2007), 547–550.

I(43) M.N. Daif and M.S. Tammam El-Sayiad,On generalized derivations of semiprime rings with involution,Internat. J. Al-gebra1 (2007), 551–555.

I(44) A.K. Faraj and A.H. Majeed, On Left σ-centralizers of Jordan ideals and generalized Jordan left (σ, τ)-derivations of prime rings, Eng. and Tech. Journal29(2011), 544–553.

I(45) A. Foˇsner and N. Perˇsin, On certain functional equation related to two-sided centralizers, Aeq. Math. 85 (2013), 329– 346.

I(46) A. Foˇsner and J. Vukman, Some functional equations on standard operator algebras,Acta Math. Hung.118(2008), 299– 306.

I(47) M. Foˇsner and J. Vukman, An equation related to two-sided centralizers in prime rings, Rocky Mountain J. Math.41 (2011), 765–776.

I (48) O. G¨olba¸si and E. Ko¸c, Notes on Jordan (σ, τ)∗ -derivations and Jordan triple (σ, τ)∗-derivations, Aeq. Math. Aeq. Math. 85 (2013), 581–591.

I(49) M. Hongan, N.U. Rehman and R.M. Al-Omary On Lie Ideals and Jordan triple derivations in rings,Rend. Sem. Mat. Univ. Padova125 (2011), 147–156.

I(50) I. Kosi-Ulbl and J. Vukman,An identity related to deriva-tions of standard operator algebras and semisimpleH∗-algebras,

CUBO A Math. J.12 (2010), 95–102.

I (51) X.F. Qi, Characterization of centralizers on rings and operator algebras,Acta Math. Sin. 56(2013), 459–468.

I(52) X.F. Qi, S.P. Du and J.C. Hou, Two kinds of additive maps on operator algebras, J. Shanxi Normal Univ. Nat. Sci. Ed.20(2006), 1–3.

I(53) X. Qi, S. Du and J. Hou,Characterization of centralizers,

Acta Math. Sin., Chin. Ser. 51(2008), 509–516.

I(54) X. Qi and J. Hou,Characterizing centralizers and gener-alized derivations on triangular algebras by acting on zero prod-uct,Acta Math. Sin., Eng. Ser. 29(2013), 1245–1256.

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I (55) N. ur Rehman, Jordan triple (α, β)∗-derivations on semiprime rings with involution, Hacettepe J. Math. Stat. 42 (2013), 641–651.

I (56) N. ˇSirovnik and J. Vukman, A result concerning two-sided centralizers on algebras with involution, Oper. Matrices 7 (2013), 687–693.

I(57) N. ˇSirovnik and J. Vukman, On derivations of operator algebras with involution, Demonstr. Math.47(2014), 784–790.

I(58) Z. Ullah and M.A. Chaudhry, θ-centralizers of rings with involution,Int. J. Algebra 4 (2010), 843–850.

I (59) J. Vukman, An equation on operator algebras and semisimpleH∗-algebras, Glasnik Math.40 (2005), 201–206.

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