[PDF] Top 20 Some Inequalities for Commutators of Bounded Linear Operators in Hilbert Spaces

... Remark 4 . It is well known that for a self-adjoint operator A and for a positive number a we have kAk ≤ a if and only if −a · I ≤ A ≤ a · I. This is also equivalent to the condition σ (A) ⊆ [−a, a] , where σ (A) denotes ... See full document

... new inequalities for the operator norm and numerical radius of sums of bounded linear operators in Hilbert ...two bounded linear operators and their applications ... See full document

... We recall that a bounded linear operator T : H → H is called strongly c 2 - accretive (with c 6= 0) if Re hT y, yi ≥ c 2 for each y ∈ H, kyk = 1. For c = 0, the operator is called accretive. Therefore, and ... See full document

... involved operators A and B (or certain expressions constructed with these operators), we establish in this paper some natural inequalities of the ... See full document

... Remark 2. The above Remark 1 shows that any bounded linear operator has the uniform (α, β)-property for infinitely many (α, β) appropriately chosen. For a given operator satisfying an (α, β)-property, it is ... See full document

... [35] J.E. Peˇ cari´ c, S.Puntanen and G. P. H Styan, . Some further matrix extensions of the Cauchy- Schwarz and Kantorovich inequalities, with some statistical applications. Special issue hon- oring ... See full document

... involved operators A and B or certain expressions constructed with these operators, we establish in this paper some natural inequalities of the ... See full document

... establish some connections that exist between the numerical radius w (A) , operator norm kAk and the semi- inner products hA, Ii p,n and hA, Ii p,w with p ∈ {i, s} that can be naturally defined on the Banach ... See full document

... Dragomir, Inequalities for the numerical radius, the norm and the maximum of the real part of bounded linear operators in Hilbert spaces.. Linear Algebra Appl.[r] ... See full document

... Furuta inequalities for power series of bounded linear operators in Hilbert spaces are ...normal operators and some functions of interest such as the exponential, ... See full document

... Dragomir, Some inequalities of the Gr¨ uss type for the numerical radius of bounded linear operators in Hilbert spaces, Preprint, RGMIA Res.. Gustafson and D.K.M.[r] ... See full document

... (1.13) w (T ) = sup {|λ| , λ ∈ W (T )} = sup {|hT x, xi| , kxk = 1} . It is well known that w (·) is a norm on the Banach algebra B (H) of all bounded linear operators T : H → H. This norm is ... See full document

... Some of the obtained results are based on recent reverse results for the Schwarz inequality in Hilbert spaces due to the author1. Numerical radius, Bounded linear operators, Normal opera[r] ... See full document

... Vector inequalities for powers of some operators in Hilbert spaces with applications for operator norm, numerical radius, commutators and self- commutators are given1. The numerical rang[r] ... See full document

... other inequalities between the operator norm and its numerical ...as some results for vectors in inner product spaces due to Goldstein-Ryff- Clarke [9], Dragomir-S´ andor [7] and Dragomir ... See full document

... We next recall some definitions and basic facts about Orlicz spaces needed for the proofs of the main results. For further information on this subject, we refer to []. A function A : [, +∞) → [, +∞) is ... See full document

... related inequalities in inner product spaces (II), ...Dragomir, Inequalities for the norm and the numerical radius of linear operators in Hilbert spaces, Demonstratio ... See full document

... (f (s) − f (t)) (g (s) − g (t)) ≥ (≤) 0 which concludes the proof. Corollary 1. If the continuous functions f, g : J → R have the same mono- tonicity on J then for any A and B two commuting bounded selfadjoint ... See full document

... Let A be a selfadjoint linear operator on a complex Hilbert space (H; h., .i) . The Gelfand map establishes a ∗-isometrically isomorphism Φ between the set C (Sp (A)) of all continuous functions defined on ... See full document

... selfadjoint linear operator on a complex Hilbert space (H; h :; : i ) : The Gelfand map establishes a -isometrically isomorphism between the set C (Sp (A)) of all continuous functions de…ned on the spectrum ... See full document