Jensen's Operator Inequality |
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Authors: | Hansen, Frank Pedersen, Gert K. |
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Affiliation: | Institute of Economics, University of Copenhagen, Studiestraede 6 DK-1455 Copenhagen K, Denmark; frank.hansen{at}econ.ku.dk Department of Mathematics, University of Copenhagen, Universitetsparken 5 DK-2100 Copenhagen Ø, Denmark; gkped{at}math.ku.dk |
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Abstract: | Jensen's operator inequality and Jensen's trace inequality forreal functions defined on an interval are established in whatmight be called their definitive versions. This is accomplishedby the introduction of genuine non-commutative convex combinationsof operators, as opposed to the contractions considered in earlierversions of the theory by the authors, and by Brown and Kosaki.As a consequence, one no longer needs to impose conditions onthe interval of definition. It is shown how this relates tothe pinching inequality of Davis, and how Jensen's trace inequalitygeneralizes to C*-algebras. 2000 Mathematics Subject Classification47A56 (primary), 46L10, 47C15, 26A51 (secondary). |
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