Non-commutativef-divergence functional

DOI10.1002/mana.201200194zbMath1446.47004arXiv1301.7349OpenAlexW2127625232MaRDI QIDQ2862563

Mohsen Kian, Mohammad Sal Moslehian

Publication date: 15 November 2013

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.7349

zbMATH Keywords

information theoryKullback-Leibler distanceoperator convexityperspective function$f$-divergence functionalCsiszár's result

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Linear operator inequalities (47A63) Inequalities for sums, series and integrals (26D15) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)

Related Items (10)

Asymmetric Choi–Davis inequalities ⋮ Lipschitz type inequalities for noncommutative perspectives of operator monotone functions in Hilbert spaces ⋮ Jointly convex mappings related to Lieb's theorem and Minkowski type operator inequalities ⋮ A generalization of \(f\)-divergence measure to convex functions defined on linear spaces ⋮ Vector joint majorization and generalization of Csiszár-Körner's inequality for \(f\)-divergence ⋮ A characterization of mean values for Csiszár's inequality and applications ⋮ Inequalities involving superquadratic functions and operators ⋮ Complementary to Jensen's operator inequalities in external formulas ⋮ A simplified and unified generalization of some majorization results ⋮ Shannon like inequalities for \(f\)-connections of positive linear maps and positive operators

Cites Work

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• Higher order optimal approximation of Csiszar's \(f\)-divergence
• A matrix convexity approach to some celebrated quantum inequalities
• Some majorization inequalities for convex functions of several variables
• Jensen's operator inequality and its converses
• Perspectives of matrix convex functions

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