[PDF] Top 20 Reverse Jensen’s type Trace Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces
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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 ... See full document
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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] ... See full document
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Some Inequalities for Convex 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 ... See full document
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Some Slater's Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Spaces
... a convex and differentiable function on ˚ I (the interior of I) whose derivative f 0 is continuous on ˚ I ...a selfadjoint operators on the Hilbert space H with Sp (A) ⊆ [m, M ] ⊂ ˚ I, ... See full document
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Jensen’s type trace inequalities for convex functions of selfadjoint operators in Hilbert spaces
... Remark 2.1. The inequality (2.3) is obviously not as good as the first part of (1.12). However it is the natural alternative of Jensen’s inequality for trace and provides simple and nice examples for various ... See full document
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Some inequalities of Čebyšev type for functions of operators in Hilbert spaces
... bounded selfadjoint operators on the complex Hilbert space H, then there exists a bounded selfadjoint operator S on H and two bounded functions ϕ and ψ such that A = ϕ (S) ... See full document
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Some Jensen's Type Inequalities for Twice Differentiable Functions of Selfadjoint Operators in Hilbert Spaces
... Theorem 4. Let A be a positive definite 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 twice differentiable function on (m, M ) and for p ∈ ... See full document
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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 Sp (A) , an the C ∗ -algebra C ∗ (A) generated by A and the identity ... See full document
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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 ... See full document
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Cebyšev’s type inequalities for positive linear maps of selfadjoint operators in Hilbert spaces
... [12] S. S. Dragomir, J. Pečarić and J. Sándor, The Chebyshev inequality in pre-Hilbertian spaces. II. Proceedings of the Third Symposium of Mathematics and its Applications (Timişoara, 1989), 75–78, ... See full document
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Recent developments of Schwarz's type trace inequalities for operators in Hilbert spaces
... bounded selfadjoint operator on H can be defined as follows, see for instance [56, ...is selfadjoint and positive, then there exists a unique positive selfadjoint operator B := √ A ∈ B (H) such that ... See full document
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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 ... See full document
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OPERATOR JENSEN’S INEQUALITY FOR OPERATOR SUPERQUADRATIC FUNCTIONS
... superquadratic functions for positive Hilbert space operators are introduced and ...A Jensen type inequality is ...several trace inequalities for superquadratic ... See full document
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Trace Inequalities of Lipschitz Type for Power Series of Operators on Hilbert Spaces
... the interval [0, R) and since the function ψ(t) := ∥ (1 − t)T + tV ∥ is convex on [0, 1] we have that f a ′ ◦ ψ is also convex on [0, 1]. Utilising the Hermite- Hadamard inequality for convex ... See full document
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Čebyšev's Type Inequalities for Functions of Selfadjoint Operators in Hilbert Spaces
... 0, s < 0 or r < 0, s > 0, then the reverse inequality holds in ...n Operators The following different version of the ˇ Cebyˇ sev inequality for a sequence of oper- ators also ... See full document
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Grüss' Type Inequalities 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 Sp (A) , an the C ∗ -algebra C ∗ (A) generated by A and the identity ... See full document
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Trace inequalities of Cassels and Grüss type for operators in Hilbert spaces
... a selfadjoint operator on the Hilbert space H and assume that Sp (A) ⊆ [m, M] for some scalars m, M with 0 < m < ...differentiable convex function on [m, M] with f 0 (m) > 0 and P ∈ B 1 (H) ... See full document
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Some inequalities of Jensen type for operator convex functions in Hilbert spaces
... The Jensen inequality for convex functions plays a crucial role in the Theory of Inequal- ities due to the fact that other inequalities such as that arithmetic mean-geometric mean inequality, ... See full document
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Some New Grüss' Type Inequalities 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 Sp (A) , an the C ∗ -algebra C ∗ (A) generated by A and the identity ... See full document
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Order generalised gradient and operator inequalities
... operator-valued functions, which is a generalisation of () (without the assumption of convexity) in the settings of bounded self-adjoint operators on a Hilbert ...some inequalities of ... See full document
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