[PDF] Top 20 Some Vector Inequalities for Continuous Functions of Self Adjoint Operators in Hilbert Spaces

... the Hilbert space H and A is a self-adjoint operator with SpA ⊆ m, M, and provide different bounds for some classes of continuous functions f : m, M → ...for some ... See full document

... type inequalities for selfadjoint operators in Hilbert ...spaces. Some of the obtained results improve the inequalities ...power functions and the logarithmic function are ... See full document

... the continuous functional calculus for a selfadjoint operator ...valued continuous function on Sp (A), then f (t) ≥ 0 for any t ∈ Sp (A) implies that f (A) ≥ 0, ...valued functions on Sp (A) then the ... See full document

... Suppose that I is an interval of real numbers with interior ˚ I and f : I → R is a convex function on I. Then f is continuous on ˚ I and has finite left and right derivatives at each point of˚ I. Moreover, if x, y ... See full document

... complex Hilbert space (H; ...all 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 on H ... See full document

... linear operators acting on a Hilbert space ( H , h·, ...For self-adjoint operators A, B ∈ B ( H ) we say that A ≤ B if B − A ≥ ...all continuous functions on the spectrum ... See full document

... If either r > 0, s < 0 or r < 0, s > 0, then the reverse inequality holds in (3.5). 4. Another Version of the ˇ Cebyˇ sev Inequality for n Operators The following different version of the ˇ Cebyˇ sev ... See full document

... 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 ... See full document

... type inequalities for selfadjoint operators in Hilbert ...spaces. Some of the obtained results improve the inequalities ...power functions and the logarithmic function are ... See full document

... 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

... 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

... 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 for f -divergence see [2], [7]- [12] and [13] Motivated by the above results, in this paper we obtain some new inequalities for quantum f - divergence of trace class ... See full document

... paper some new bounds for the magnitude of C f , in the case when one of the complex valued function, say f , is convex in absolute value while the other is Lebesgue integrable on [a, b] ...for functions of ... See full document

... 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 A; denoted Sp (A) ; an ... See full document

... 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 ... See full document

... the continuous functions f, g : J → R are synchronous on J and one of them is convex while the other is concave, then we have the improvement of the inequality ... See full document

... 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 ... See full document

... linear operators acting on a Hilbert space ( H , h·, ...For self-adjoint operators A, B ∈ B ( H ) we say that A ≤ B if B − A ≥ ...all continuous functions on the spectrum ... 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 Mathematica ... See full document