Some operator and trace function convexity theorems

DOI10.1016/j.laa.2015.11.006zbMath1342.47024arXiv1409.0564OpenAlexW2963582288MaRDI QIDQ898796

Elliott H. Lieb, Rupert L. Frank, Eric Anders Carlen

Publication date: 18 December 2015

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.0564

zbMATH Keywords

trace inequalityoperator convexityRényi entropyoperator concavity

Mathematics Subject Classification ID

Linear operator inequalities (47A63) Measures of information, entropy (94A17) Basic linear algebra (15A99)

Related Items (15)

Convexity of a certain operator trace functional ⋮ Matrix analysis and quantum information ⋮ A pedagogical intrinsic approach to relative entropies as potential functions of quantum metrics: The \(q\)-\(z\) family ⋮ Generalizing Lieb's concavity theorem via operator interpolation ⋮ Lieb type convexity for positive operator monotone decreasing functions ⋮ Different quantum f-divergences and the reversibility of quantum operations ⋮ Some convexity and monotonicity results of trace functionals ⋮ Strengthened convexity of positive operator monotone decreasing functions ⋮ Inequalities for quantum divergences and the Audenaert–Datta conjecture ⋮ Trace minmax functions and the radical Laguerre-Pólya class ⋮ Variational representations related to quantum Rényi relative entropies ⋮ α-z-Rényi relative entropies ⋮ The \(\alpha\)-\(z\)-Bures Wasserstein divergence ⋮ Concavity of certain matrix trace and norm functions. II. ⋮ From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture

Cites Work

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• A Minkowski type trace inequality and strong subadditivity of quantum entropy. II: Convexity and concavity
• Concavity of certain maps on positive definite matrices and applications to Hadamard products
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• Some operator inequalities of the Schwarz type
• Remarks on two theorems of E. Lieb
• Convex trace functions and the Wigner-Yanase-Dyson conjecture
• Concavity of certain matrix trace and norm functions
• α-z-Rényi relative entropies
• Monotonicity of a relative Rényi entropy
• Entropic Fluctuations in Quantum Statistical Mechanics. An Introduction

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