Log and harmonically log-convex functions related to matrix norms

DOI10.7153/oam-10-26zbMath1350.47007OpenAlexW2511516589MaRDI QIDQ3186694

Mohammad S. Sababheh

Publication date: 12 August 2016

Published in: Operators and Matrices (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/oam-10-26

zbMATH Keywords

convex functionsunitarily invariant norm inequalitiesHeinz meanslogconvex functions

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Convexity of real functions in one variable, generalizations (26A51)

Related Items

Matrix mixed mean inequalities ⋮ Advanced refinements of Young and Heinz inequalities ⋮ On some classical trace inequalities and a new Hilbert-Schmidt norm inequality ⋮ Means refinements via convexity ⋮ On superquadratic and logarithmically superquadratic functions ⋮ Two variables functionals and inequalities related to measurable operators ⋮ Mean Inequalities for the Numerical Radius ⋮ Norm inequalities via convex and log-convex functions ⋮ Some refinements of real power form inequalities for convex functions via weak sub-majorization ⋮ Further refinements of real power form inequalities for convex functions via weak sub-majorization ⋮ New Hilbert-Schmidt norm inequalities for positive semidefinite matrices ⋮ Convex functions and means of matrices ⋮ On the matrix harmonic mean ⋮ Composite convex functions ⋮ Quadratic interpolation of the Heinz means ⋮ Convexity and matrix means ⋮ Operator inequalities via geometric convexity ⋮ The interpolation of Young's inequality using dyadics

Cites Work

• On the convexity of the Heinz means
• Some inequalities for norms on matrices and operators
• Comparison of various means for operators
• Norm inequalities for fractional powers of positive operators
• Young type inequalities for positive operators
• Interpolated inequalities for unitarily invariant norms
• Further refinements of the Heinz inequality
• Integral inequalities of the Heinz means as convex functions
• Inequalities involving unitarily invariant norms and operator monotone functions