functions of selfadjoint operators
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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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 Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces
... For a recent monograph devoted to various inequalities for functions of selfadjoint operators, see [6] and the references therein. For other results, see [13], [7] and [9]. 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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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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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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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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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 ...
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Inequalities of Hermite-Hadamard type for functions of selfadjoint operators and matrices
... a selfadjoint linear operator on a complex Hilbert space (H; ...continuous functions defined on the spectrum of A, denoted Sp (A) , and the C ∗ - algebra C ∗ ( A ) generated by A and the identity operator 1 ...
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Some Reverses of the Jensen Inequality for Functions of Selfadjoint Operators in Hilbert Spaces
... a selfadjoint linear operator on a complex Hilbert space H; ·, ...continuous functions defined on the spectrum of A, denoted SpA, and the C ∗ -algebra C ∗ A generated by A and the identity operator 1 H on H ...
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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 Inequalities for the Čebyšev Functional of Two Functions of Selfadjoint Operators in Hilbert Spaces
... 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 ...
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Some Jensen's Type Inequalities for Twice Differentiable Functions of Selfadjoint Operators in Hilbert Spaces
... a selfadjoint linear operator on a complex Hilbert space (H; ...continuous functions defined on the spectrum of A, denoted Sp (A) , an the C ∗ -algebra C ∗ (A) generated by A and the identity operator 1 H ...
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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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Trace inequalities of Shisha-Mond type for operators in Hilbert spaces
... Dragomir, Reverse Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces.. Fink, A treatise on Grüss’ inequality, Analytic and Geometric Inequal[r] ...
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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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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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Trace inequalities of Cassels and Grüss type for operators in Hilbert spaces
... Proposition 1 Let A be a selfadjoint operator on the Hilbert space H and assume that Sp (A) ⊆ [m, M] for some scalars m, M with 0 < m < M. If f is a continuously differentiable convex function on [m, M] with ...
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Inequalities for the Riemann-Stieltjes integral of S-dominated integrators with applications. I
... Proposition 2. Let A be a bounded selfadjoint operator on the Hilbert space H. Denote m := min {λ |λ ∈ Sp (A) } = min Sp (A) and M := := max {λ |λ ∈ Sp (A) } = max Sp (A) . If f : R → C is a continuous function on ...
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KLEIN’S TRACE INEQUALITY AND SUPERQUADRATIC TRACE FUNCTIONS
... quadratic functions does not need to be ...convex functions and second to present some counterpart results concerning convex ...superquadratic functions are power ...
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