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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

Abstract:

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: https://doi.org/10.1090/S0002-9939-1987-0870784-0
  • MathSciNet review: 870784