Operator monotone functions, positive definite kernels and majorization

DOI10.1090/S0002-9939-10-10386-4zbMath1225.47016MaRDI QIDQ3056542

Mitsuru Uchiyama

Publication date: 12 November 2010

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

zbMATH Keywords

operator monotone functionmajorizationpositive definite kernelmatrix orderpick functionLöwner theoreminfinitely divisible kernel

Mathematics Subject Classification ID

Linear inequalities of matrices (15A39) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Kernel operators (47B34)

Related Items (23)

Furuta type inequalities via operator means and applications to Kadison's type inequalities ⋮ Some results on strongly operator convex functions and operator monotone functions ⋮ Operator means and positivity of block operators ⋮ Monotone norms and Finsler structures in noncommutative spaces ⋮ Optimal Self-Concordant Barriers for Quantum Relative Entropies ⋮ Ruminations on matrix convexity and the strong subadditivity of quantum entropy ⋮ Operator log-convex functions and operator means ⋮ Loewner matrices of matrix convex and monotone functions ⋮ Some operator inequalities involving operator monotone functions ⋮ Operator inequalities: from a general theorem to concrete inequalities ⋮ Superadditivity and derivative of operator functions ⋮ The principal inverse of the gamma function ⋮ Convexity of quasi-entropy type functions: Lieb's and Ando's convexity theorems revisited ⋮ Positive linear maps on \(C^\ast\)-algebras and rigid functions ⋮ Inverses of Operator Convex Functions ⋮ Higher order extension of Löwner’s theory: Operator 𝑘-tone functions ⋮ A converse of Loewner-Heinz inequality and applications to operator means ⋮ Inequalities for generalized derivations of operator monotone functions in norm ideals of compact operators ⋮ Operator functions and the operator harmonic mean ⋮ From positive to accretive matrices ⋮ Some results on matrix means ⋮ Symmetric matrix means ⋮ Separated spectra and operator inequalities

Cites Work

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• Über konvexe Matrixfunktionen
• A New Majorization Induced by Matrix Order
• Matrix Analysis
• Inverse functions of polynomials and orthogonal polynomials as operator monotone functions
• Infinitely Divisible Matrices
• The Theory of Infinitely Divisible Matrices and Kernels
• On Analytic Continuation to a Schlicht Function
• On Boundary Values of a Schlicht Mapping
• Monotone and Convex Operator Functions

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