On the equality in Jensen's inequality for operator convex functions

DOI10.1007/BF01195811zbMath0638.46040OpenAlexW2131593110MaRDI QIDQ1099374

Dénes Petz

Publication date: 1986

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01195811

zbMATH Keywords

operator convex functionpositive unit preserving linear map

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05)

Related Items (9)

Revisiting the equality conditions of the data-processing inequality for the sandwiched Rényi divergence ⋮ Two-moment characterization of spectral measures on the real line ⋮ ON EQUALITY CONDITION FOR TRACE JENSEN INEQUALITY IN SEMI-FINITE VON NEUMANN ALGEBRAS ⋮ An entropic uncertainty principle for positive operator valued measures ⋮ Positive linear maps on \(C^\ast\)-algebras and rigid functions ⋮ The noncommutative Choquet boundary. II: Hyperrigidity ⋮ Reduced commutativity of moduli of operators ⋮ Quantum hypothesis testing and sufficient subalgebras ⋮ Non-commutativef-divergence functional

Cites Work

• Unnamed Item
• Jensen's inequality for operators and Loewner's theorem
• A Schwarz inequality for positive linear maps on C\(^*\)-algebras
• Positive linear maps of operator algebras
• Conditional expectations in von Neumann algebras
• A Schwarz Inequality for Convex Operator Functions
• A note on the entropy for operator algebras
• Operator-valued entropy of a quantum mechanical measurement
• A functional method on amount of entropy
• Positive Functions on C ∗ -Algebras
• Monotone and Convex Operator Functions

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