On matrix inequalities between the power means: counterexamples

DOI10.1016/j.laa.2013.04.012zbMath1283.15061arXiv1302.7040OpenAlexW2963587837WikidataQ124841705 ScholiaQ124841705MaRDI QIDQ2637143

Fumio Hiai, Koenraad M. R. Audenaert

Publication date: 19 February 2014

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

Full work available at URL: https://arxiv.org/abs/1302.7040

zbMATH Keywords

Jensen inequalityjoint convexitysymmetric normmatrix power mean inequality

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Miscellaneous inequalities involving matrices (15A45) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items

Matrix Inequalities and Characterizations of Operator Monotone Functions, Concavity of certain matrix trace and norm functions, On certain order properties of non Kubo-Ando means in operator algebras, Matrix power means and new characterizations of operator monotone functions, Developed matrix inequalities via positive multilinear mappings, A new type of operator convexity, Some inequalities involving positive linear maps under certain conditions, Some inequalities for operator (p, h)-convex functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Norm inequalities related to the matrix geometric mean
• Jensen's inequality for operators without operator convexity
• Some inequalities for positive linear maps
• Jensen's inequality for operators and Loewner's theorem
• A Schwarz inequality for positive linear maps on C\(^*\)-algebras
• Means of positive linear operators
• Matrix Analysis: Matrix Monotone Functions, Matrix Means, and Majorization
• NORM AND ANTI-NORM INEQUALITIES FOR POSITIVE SEMI-DEFINITE MATRICES
• A Schwarz Inequality for Convex Operator Functions
• Inequalities between means of positive operators