Operator functions and the operator harmonic mean

DOI10.1090/proc/14753zbMath1491.47017OpenAlexW2959395378MaRDI QIDQ5210951

Mitsuru Uchiyama

Publication date: 16 January 2020

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/14753

zbMATH Keywords

operator monotone functionsLoewner theoremstrongly operator convex functionsoperator harmonic mean

Mathematics Subject Classification ID

Linear inequalities of matrices (15A39) Linear operator inequalities (47A63) Functional calculus for linear operators (47A60) Convexity of real functions in one variable, generalizations (26A51)

Related Items (6)

Generalized parallel sum of adjointable operators on Hilbert C*-modules ⋮ Geometric Mean and Matrix Quadratic Equations ⋮ Some operator inequalities involving operator monotone functions ⋮ Operator means and matrix quadratic equations ⋮ Some results on matrix means ⋮ Symmetric matrix means

Cites Work

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• Operator log-convex functions and operator means
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• Means of positive linear operators
• Some results on strongly operator convex functions and operator monotone functions
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• A treatment of strongly operator-convex functions that does not require any knowledge of operator algebras
• Über monotone Matrixfunktionen
• Series and parallel addition of matrices
• Operator monotone functions, positive definite kernels and majorization
• A Schwarz Inequality for Convex Operator Functions
• Loewner's Theorem on Monotone Matrix Functions

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