Reduced relative quantum entropy [PDF]
arXiv, 2022 We introduce the notion of reduced relative quantum entropy and prove that it is convex. This result is then used to give a simplified proof of a theorem of Lieb and Seiringer.
arxiv
On a Quantum Entropy Power Inequality of Audenaert, Datta and Ozols [PDF]
, 2016 We give a short proof of a recent inequality of Audenaert, Datta and Ozols, and determine cases of equality.
arxiv +1 more source
Perturbation of Schauder frames and besselian Schauder frames in Banach spaces [PDF]
arXiv, 2023 We consider the stability of Schauder frames and besselian Schauder frames under perturbations. Our results are inspirit close to the results of Heil [18].
arxiv
Symmetric norms and reverse inequalities to Davis and Hansen-Pedersen characterizations of operator convexity [PDF]
arXiv, 2005 Some rearrangement inequalities for symmetric norms on matrices are given as well as related results for operator convex functions.
arxiv
A note on Khabibullin's conjecture for integral inequalities [PDF]
arXiv, 2010 An integral transformation relating two inequalities in Khabibullin's conjecture is found. Another proof of this conjecture for some special values of its numeric parameters is suggested.
arxiv
Characterization of operator convex functions by certain operator inequalities
Mathematical Inequalities & Applications, 2019 For λ ∈ (0,1) , let ψ be a non-constant, non-negative, continuous function on (0,∞) and let Γλ (ψ) be the set of all non-trivial operator means σ such that an inequality ψ(A∇λ B) ψ(A)σψ(B) holds for all A,B ∈ B(H)++ . Then we have: 1.
H. Osaka, Yukihiro Tsurumi, Shuhei Wada
semanticscholar +1 more source
Power vector inequalities for operator pairs in Hilbert spaces and their applications
Open MathematicsThis study explores the power vector inequalities for a pair of operators (B,C)\left(B,C) in a Hilbert space. By utilizing a Mitrinović-Pečarić-Fink-type inequality for inner products and norms, we derive various power vector inequalities.
Altwaijry Najla +2 more
doaj +1 more source
Weighted norm inequalities for fractional oscillatory integrals and applications [PDF]
arXiv, 2011 We set up some weighted norm inequalities for fractional oscillatory integral operators. As applications, the corresponding results for commutators formed by $BMO(\mathbb{R}^{n})$ functions and the operators are established.
arxiv
An extension of the Golden-Thompson theorem
, 2014 In this paper, we shall prove |treA+B|≤tr(|eA||eB|) for normal matrices A, B. In particular, treA+B≤tr(eAeB) if A, B are Hermitian matrices, yielding the Golden-Thompson inequality.MSC:15A16, 47A63, 15A45.
Hongyi Li, Di Zhao
semanticscholar +1 more source
Some new Hermite-Hadamard type inequalities for two operator convex functions [PDF]
arXiv, 2012 In this paper we establish some new Hermite-Hadamard type inequalities for two operator convex functions of selfadjoint operators in Hilbert spaces.
arxiv