Jensen’s inequality for positive contractions on operator algebras

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Abstract

Let T be a normal semifinite trace on a von Neumann algebra, and let f be a continuous convex function on the interval [0, ∞) with f(0) = 0. For a positive element a of the algebra and a positive contraction α on the algebra, the following inequality is obtained: T(f(α(a))) ≤ T(α(f(a))).

Original languageEnglish
Pages (from-to)273-277
Number of pages5
JournalProceedings of the American Mathematical Society
Volume99
Issue number2
DOIs
Publication statusPublished - 1987

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Keywords

  • Convex function
  • Jensen’s inequality
  • Trace
  • Von Neumann algebra

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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