Proceedings of the American Mathematical Society

Author(s): Frank Hansen
Journal: Proc. Amer. Math. Soc. 125 (1997), 2093-2102.
MSC (1991): Primary 47A63; Secondary 47A80, 47Bxx
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract: The operator convex functions of two variables are characterized in terms of a non-commutative generalization of Jensen's inequality.

1.: W.N. Anderson, Jr., Shorted operators, SIAM J. Appl. Math., 20:520-525, 1971. MR 44:5172
2.: T. Ando, Concavity of certain maps of positive definite matrices and applications to adamard products, Linear Algebra Appl., 26:203-241, 1979. MR 80f:15023
3.: J.S. Aujla, Matrix convexity of functions of two variables, Linear Algebra and Its Applications, 194:149-160, 1993.
4.: J. Bendat and S. Sherman, Monotone and convex operator functions, Trans. Am. Math. Soc., 79:58-71, 1955. MR 18:588b
5.: F. Hansen, An operator inequality, Math. Ann., 246:249-250, 1980. MR 82a:46065
6.: F. Hansen, Extrema for concave operator mappings, Math. Japonica., 40:331-338, 1994. MR 95h:47019
7.: F. Hansen and G.K. Pedersen, Jensen's inequality for operators and öwner's theorem, Math. Ann., 258:229-241, 1982. MR 83g:47020
8.: F. Hartogs, Zur heorie der analytischen unktionen mehrerer unabhängiger eränderlichen, inbesonderere über die arstellung derselben durch eihen, welche nach otenzen einer eränderlichen fortschreiten, Math. Ann., 62:1-88, 1906.
9.: R.V. Kadison and J.R. Ringrose, Fundamentals of the Theory of Operator Algebras, I-II, Academic Press, 1982 & 1986.
10.: A. Korányi, On some classes of analytic functions of several variables, Trans Amer. Math. Soc., 101:520-554, 1961. MR 25:226
11.: F. Kraus, Über konvekse atrixfunktionen, Math. Z., 41:18-42, 1936.
12.: K. Löwner, Über monotone atrixfunktionen, Math. Z., 38:177-216, 1934.
13.: H. Vasudeva, On monotone matrix functions of two variables, Trans. Amer. Math. Soc., 176:305-318, 1973. MR 47:2408

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A63, 47A80, 47Bxx

Frank Hansen
Affiliation: Institute of Economics, University of Copenhagen, Studiestraede 6, DK-1455 Copenhagen K, Denmark

DOI: 10.1090/S0002-9939-97-04003-3
PII: S 0002-9939(97)04003-3
Received by editor(s): February 2, 1996
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1997, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS