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JENSEN'S OPERATOR INEQUALITY

Published online by Cambridge University Press:  09 June 2003

FRANK HANSEN  and
GERT K. PEDERSEN
FRANK HANSEN
Affiliation:
Institute of Economics University of Copenhagen Studiestraede 6 DK-1455 Copenhagen K Denmarkfrank.hansen@econ.ku.dk
GERT K. PEDERSEN
Affiliation:
Department of Mathematics University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen Ø Denmarkgkped@math.ku.dk
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Abstract

Jensen's operator inequality and Jensen's trace inequality for real functions defined on an interval are established in what might be called their definitive versions. This is accomplished by the introduction of genuine non-commutative convex combinations of operators, as opposed to the contractions considered in earlier versions of the theory by the authors, and by Brown and Kosaki. As a consequence, one no longer needs to impose conditions on the interval of definition. It is shown how this relates to the pinching inequality of Davis, and how Jensen's trace inequality generalizes to C*-algebras.

Keywords

47A56 (primary)46L1047C1526A51 (secondary)
Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 4 , July 2003 , pp. 553 - 564
Copyright
© The London Mathematical Society 2003

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