On the equality in Jensen's inequality for operator convex functions
type: Item
instance of: scholarly article
title: On the equality in Jensen's inequality for operator convex functions
zbMATH Open document ID: 0638.46040
DOI: 10.1007/BF01195811
published in: Integral Equations and Operator Theory
publication date: 1986-01-01T00:00:00Z
review text: Let \(A,B\) be unital \(C^*\)-algebras, and let \(\Phi:A\to B\) be a positive unit preserving linear map. \textit{M. D. Choi} [Ill. J. Math. 18, 565-574 (1974; Zbl 0293.46043)] has proved that \(f(\Phi(a))\leq \Phi(f(a))\) for all self-adjoint \(a\in A\) with \(Sp(a)\subset (\alpha,\beta)\) and \(f:(\alpha,\beta)\to {\mathbb{R}}\) an operator convex function. This paper proves that equality holds if and only if \(\Phi\) restricted to the subalgebra generated by a is multiplicative.
reviewed by: W. Moran
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 4040587
zbMATH Keywords: positive unit preserving linear map
zbMATH Keywords: operator convex function
author: Dénes Petz
MaRDI profile type: Publication
cites work: Q4169818
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full work available at URL: https://doi.org/10.1007/bf01195811
OpenAlex ID: W2131593110
description: scientific article; zbMATH DE number 4040587