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Proceedings of the American Mathematical Society

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

 
 

 

Jensen’s inequality for positive contractions on operator algebras


Author: Dénes Petz
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
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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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Keywords: Convex function, trace, von Neumann algebra, Jensen’s inequality
Article copyright: © Copyright 1987 American Mathematical Society