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Jensen's Inequality for Positive Contractions on Operator Algebras

Dénes Petz
Proceedings of the American Mathematical Society
Vol. 99, No. 2 (Feb., 1987), pp. 273-277
DOI: 10.2307/2046624
Stable URL: http://www.jstor.org/stable/2046624
Page Count: 5
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Jensen's Inequality for Positive Contractions on Operator Algebras
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Abstract

Let τ be a normal semifinite trace on a von Neumann algebra, and let f be a continuous convex function on the interval [ 0, ∞) with f(0) = 0. For a positive element a of the algebra and a positive contraction α on the algebra, the following inequality is obtained: τ(f(α(a))) ≤ τ(α(f(a))).

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