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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Jensen's operator inequality
for functions of several variables


Authors: Huzihiro Araki and Frank Hansen
Journal: Proc. Amer. Math. Soc. 128 (2000), 2075-2084
MSC (1991): Primary 47A63; Secondary 47A80, 47Bxx
Published electronically: February 16, 2000
MathSciNet review: 1670414
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Abstract: The operator convex functions of several variables are characterized in terms of a non-commutative generalization of Jensen's inequality, extending previous results of F. Hansen and G.K. Pedersen for functions of one variable and of F. Hansen for functions of two variables.


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Additional Information

Huzihiro Araki
Affiliation: Department of Mathematics, Faculty of Science and Technology, The Science University of Tokyo, Noda, Chiba-ken 278-8510, Japan
Email: araki@ma.noda.sut.ac.jp

Frank Hansen
Affiliation: Institute of Economics, University of Copenhagen, Studiestraede 6, 1455 Copenhagen K, Denmark
Email: frank.hansen@econ.ku.dk

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05371-5
PII: S 0002-9939(00)05371-5
Received by editor(s): August 30, 1998
Published electronically: February 16, 2000
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society