Around operator monotone functions
type: Item
instance of: scholarly article
title: Around operator monotone functions
zbMATH Open document ID: 1272.47026
author: Mohammad Sal Moslehian
author: Hamed Najafi
published in: Integral Equations and Operator Theory
publication date: 2012-06-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/1110.6594
review text: There has been considerable interest in obtaining sub-additive (super-additive) inequalities for matrix functions analogous to the sub-additive (super-additive) inequality for concave (convex) functions of the reals. If the function \(f:[0,\infty )\rightarrow [0,\infty )\) is operator concave, then the sub-additive inequality \(f(A+B)\leq f(A)+f(B)\) does not hold in general for positive semidefinite \(n\times n\) matrices \(A,B\). In this paper, the authors prove that this sub-additive inequality holds if and only if the symmetrized product \(AB+BA\) is positive semidefinite. The authors also give a necessary and sufficient condition that the composition \(f\circ g\) of an operator convex function \(f\) on \([0,\infty )\) and a non-negative operator monotone function \(g\) on an interval \((a,b)\) is operator monotone. Some applications are also given.
reviewed by: Jaspal Singh Aujla
Mathematics Subject Classification ID: 47A63
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47A30
zbMATH DE Number: 6048412
zbMATH Keywords: operator monotone function
zbMATH Keywords: Jordan product
zbMATH Keywords: operator convex function
zbMATH Keywords: subadditivity
zbMATH Keywords: composition of functions
MaRDI profile type: Publication
OpenAlex ID: W2004185483
arXiv ID: 1110.6594
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DOI: 10.1007/S00020-011-1921-0
description: scientific article; zbMATH DE number 6048412