Selfadjoint operators
Some Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces
... Theorem 2 (Dragomir, 2008, [3]). Let I be an interval and f : I → R be a convex and differentiable function on ˚ I (the interior of I) whose derivative f 0 is continuous on ˚ I . If A is a selfadjoint ...
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Reverse Jensen’s type Trace Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces
... bounded selfadjoint operators on the complex Hilbert space H, then there exists a bounded selfadjoint operator T on H and two bounded functions ϕ and ψ such that A = ϕ (T ) and B = ψ (T ) ...
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Some Reverses of the Jensen Inequality for Functions of Selfadjoint Operators in Hilbert Spaces
... For a recent monograph devoted to various inequalities for functions of selfadjoint operators, see [4] and the references therein. For other results, see [11], [5] and [7]. The following result that ...
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Grüss' Type Inequalities for Functions of Selfadjoint Operators in Hilbert Spaces
... Motivated by the above results we investigate in this paper other Gr¨ uss’ type inequalities for selfadjoint operators in Hilbert spaces. Some of the obtained results improve the inequalities (2.3) and ...
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Inequalities for the Čebyšev Functional of Two Functions of Selfadjoint Operators in Hilbert Spaces
... be selfadjoint operators with Sp (A) ; Sp (B) [m; M ] for some real numbers m < M: If f : [m; M ] ! R is absolutely continuous then we have the Ostrowski type inequality for selfadjoint ...
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Some Slater's Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces
... For a recent monograph devoted to various inequalities for functions of selfadjoint operators, see [7] and the references therein. For other results, see [14], [8] and [10]. The following result that ...
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Some New Grüss' Type Inequalities for Functions of Selfadjoint Operators in Hilbert Spaces
... Motivated by the above results we investigate in this paper other Gr¨ uss’ type inequalities for selfadjoint operators in Hilbert spaces. Some of the obtained results improve the inequalities (2.3) and ...
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Refinements of the Cauchy-Bunyakovsky-Schwarz Inequality for Functions of Selfadjoint Operators in Hilbert Spaces
... Theorem 4 . Let (ϕ, ψ) be a (DEC)-pair of continuous functions on [0, ∞) × [0, ∞) . If A, B are selfadjoint operators on the Hilbert space (H ; h., .i) with Sp (A) , Sp (B) ⊆ [m, M ] for some scalars m < ...
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Čebyšev's Type Inequalities for Functions of Selfadjoint Operators in Hilbert Spaces
... are selfadjoint operators and Sp (A) , Sp (B) ⊆ [m, M ] , then for any continuous synchronous (asynchronous) functions f, g : [m, M ] −→ R we have the more general ...
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Proximity Between Selfadjoint Operators and Between Their Associated Random Measures
... In order to fix notation, Section 2 is devoted to the recall of some notions, as random measure, spectral measure, space of the measurable applications of integrable square with respect to a random measure, and ...
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Inequalities of Hermite-Hadamard type for functions of selfadjoint operators and matrices
... f (( 1 − λ ) A + λ B ) ()( 1 − λ ) f ( A ) + λ f ( B ) (OC) in the operator order, for all λ ∈ [0, 1] and for every selfadjoint operator A and B on a Hilbert space H whose spectra are contained in I. Notice that a ...
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Some Reverses of the Jensen Inequality for Functions of Selfadjoint Operators in Hilbert Spaces
... Let A be a selfadjoint linear operator on a complex Hilbert space H; ·, ·. The Gelfand map establishes a ∗-isometrically isomorphism Φ between the set CSpA of all continuous functions defined on the spectrum of A, ...
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Some Inequalities for Power Series of Selfadjoint Operators in Hilbert Spaces via Reverses of the Schwarz Inequality
... a 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 of ...
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Some Jensen's Type Inequalities for Twice Differentiable Functions of Selfadjoint Operators in Hilbert Spaces
... a selfadjoint operator A. If A is a selfadjoint operator and f is a real valued continuous function on Sp (A), then f (t) ≥ 0 for any t ∈ Sp (A) implies that f (A) ≥ 0, ...
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Some Inequalities for the Čebyšev Functional of Two Functions of Selfadjoint Operators in Hilbert Spaces
... a selfadjoint operator A: If A is a selfadjoint operator and f is a real valued continuous function on Sp (A), then f (t) 0 for any t 2 Sp (A) implies that f (A) 0; i:e: f (A) is a positive operator on H: ...
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Cebyšev’s type inequalities for positive linear maps of selfadjoint operators in Hilbert spaces
... Let A be a selfadjoint operator with Sp (A) ⊆ [m, M] for some real num- bers m < M. If f, g : [m, M ] −→ R are continuous, synchronous and one is convex while the other is concave on [m, M] , then by Jensen’s ...
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Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces
... The following result provides reverses for the inequalities (2.2) and (2.3) above: Theorem 2.2. Let A be a selfadjoint operator on the Hilbert space H and assume that Sp (A) ⊆ [m, M ] for some scalars m, M with m ...
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Structure of the antieigenvectors of a strictly accretive operator
... STATIONARY VALUF OF ^I’ FOR SELFADJOINT OPERATORS For a selfadjoint operator A we can obtain the structure of the stationary vectors of RAf which is obviously equal to ^f in this case, i[r] ...
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Some Vector Inequalities for Continuous Functions of Self Adjoint Operators in Hilbert Spaces
... Dragomir, “Some Ostrowski’s type vector inequalities for functions of selfadjoint operators in Hilbert spaces,” RGMIA Research Report Collection, vol.. Dragomir, “Comparison between func[r] ...
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Norm inequalities of Čebyšev type for power series in Banach algebras
... Dragomir, SS: Inequalities for the Čebyšev functional of two functions of selfadjoint operators in Hilbert spaces.. Dragomir, SS: Some inequalities for power series of selfadjoint opera[r] ...
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