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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:

$\displaystyle \tau (f(\alpha (a))) \leq \tau (\alpha (f(a))).$


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DOI: https://doi.org/10.1090/S0002-9939-1987-0870784-0
Keywords: Convex function, trace, von Neumann algebra, Jensen's inequality
Article copyright: © Copyright 1987 American Mathematical Society

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