Jensen’s inequality for positive contractions on operator algebras

Petz, Dénes

doi:10.1090/S0002-9939-1987-0870784-0

Jensen’s inequality for positive contractions on operator algebras
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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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