[PDF] Top 20 Inequalities for Quantum f-Divergence of Trace Class Operators in Hilbert Spaces

... the quantum f -divergence when the operators P and Q satisfy the condition ...Let f : [0, ∞ ) → R be a continuous convex function that is ... See full document

... Abstract: A new quantum f -divergence for trace class operators in Hilbert Spaces is introduced. It is shown that for normalised convex functions it is nonnegative. ... 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 ... See full document

... [20] Dragomir S.S., Some Slater’s type inequalities for convex functions of selfadjoint operators in Hilbert spaces, Rev. Un. Mat. Argentina 52(2011), no. 1, 109–120. Preprint RGMIA Res. Rep. ... See full document

... R\ { 0 } . For r ∈ (− ∞ , 0) ∪ [1, ∞ ), f is convex while for r ∈ (0, 1), f is concave. Let r ≥ 1 and A be a selfadjoint operator on the Hilbert space H and assume that Sp (A) ⊆ [m, M] for some ... See full document

... Some norm inequalities for sequences of linear operators defined on Hilbert spaces that are related to the classical Schwarz inequality are given.. Applications for vector inequalities a[r] ... See full document

... the Hilbert space H and assume that Sp (A) ⊆ [m, M ] for some scalars m, M with m < ...If f is a continuously differentiable convex function on [m, M ] and B ∈ B 2 (H ) \ {0} , then we ... See full document

... 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

... 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 functions (see for ... See full document

... the Hilbert space H and assume that Sp (A) ⊆ [m, M ] for some scalars m, M with m + M 6= ...If f is a continuously differentiable convex function on [m, M ] with f 0 (m) + f 0 (M ) 6= 0 and P ... See full document

... 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: Moreover, if both f and g are real ... See full document

... difference f ( λ )f( λ xy) – f ( λ x)f ( λ y), provided that the complex number λ and the vectors x, y ∈ B are such that the series in the above expression are ... See full document

... 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 ... See full document

... the Hilbert space H and assume that Sp (A) ⊆ [m, M ] for some scalars m, M with 0 < m < ...If f is a twice differentiable function on (m, M ) and for p ∈ (−∞, 0) ∪ (1, ∞) we have for some γ < Γ ... See full document

... the inequalities obtained in the previous sections can be applied to obtain particular inequalities of interest for di¤erent selections of the functions f and g ... See full document

... other inequalities between the operator norm and its numerical ...product spaces due to Goldstein-Ryff- Clarke [9], Dragomir-S´ andor [7] and Dragomir ... 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, hyperbolic and ... See full document

... 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 ... 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 σ (A) denotes ... See full document

... Corollary 4 . Let (ϕ, ψ) be a (DEC)-pair of continuous functions on [0, ∞)× [0, ∞) . If A is a selfadjoint operator on the Hilbert space (H ; h., .i) with Sp (A) ⊆ [m, M ] for some scalars m < M and if f ... See full document