Operator maps of Jensen-type

Frank Hansen, Mohammad Sal Moslehian, Hamed Najafi

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let BJ(H) denote the set of self-adjoint operators acting on a Hilbert space H with spectra contained in an open interval J. A map Φ : BJ(H) → B(H) sa is said to be of Jensen-type if Φ(C∗AC+D∗BD)≤C∗Φ(A)C+D∗Φ(B)Dfor all A, B∈ BJ(H) and bounded linear operators C, D acting on H with CC+ DD= I, where I denotes the identity operator. We show that a Jensen-type map on an infinite dimensional Hilbert space is of the form Φ (A) = f(A) for some operator convex function f defined in J.

Original languageEnglish
Pages (from-to)1255-1263
Number of pages9
JournalPositivity
Volume22
Issue number5
DOIs
Publication statusPublished - 2018 Nov 1

Keywords

  • Convex operator function
  • Jensen’s operator inequality

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Mathematics(all)

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