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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Jensen’s inequality for positive contractions on operator algebras
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by Dénes Petz PDF
Proc. Amer. Math. Soc. 99 (1987), 273-277 Request permission


Let $\tau$ be a normal semifinite trace on a von Neumann algebra, and let $f$ be a continuous convex function on the interval $[0,\infty )$ with $f(0) = 0$. For a positive element $a$ of the algebra and a positive contraction $\alpha$ on the algebra, the following inequality is obtained: \[ \tau (f(\alpha (a))) \leq \tau (\alpha (f(a))).\]
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 99 (1987), 273-277
  • MSC: Primary 46L10
  • DOI:
  • MathSciNet review: 870784