On the equality in Jensen's inequality for operator convex functions

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Let A and B be C*-algebras with unit and assume that φ{symbol}:A→B is a positive unit preserving linear mapping. Choi proved that {Mathematical expression} if a=a*∈A and Sp(a)⊂(α, β) for every operator convex function f: (α, β) → ℝ. We prove that the equality holds if and only if φ{symbol} restricted to the subalgebra generated by {a} is multiplicative. An example is shown as an application.

Original languageEnglish
Pages (from-to)744-747
Number of pages4
JournalIntegral Equations and Operator Theory
Volume9
Issue number5
DOIs
Publication statusPublished - Sep 1986

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Jensen's inequality
Convex function
Equality
Unit
Operator
C*-algebra
Subalgebra
Multiplicative
If and only if

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

Cite this

On the equality in Jensen's inequality for operator convex functions. / Petz, D.

In: Integral Equations and Operator Theory, Vol. 9, No. 5, 09.1986, p. 744-747.

Research output: Contribution to journalArticle

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