Jensen’s operator inequality for functions of two variables
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- Proc. Amer. Math. Soc. 125 (1997), 2093-2102 Request permission
Abstract:
The operator convex functions of two variables are characterized in terms of a non-commutative generalization of Jensen’s inequality.References
- William N. Anderson Jr., Shorted operators, SIAM J. Appl. Math. 20 (1971), 520–525. MR 287970, DOI 10.1137/0120053
- T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Algebra Appl. 26 (1979), 203–241. MR 535686, DOI 10.1016/0024-3795(79)90179-4
- J.S. Aujla, Matrix convexity of functions of two variables, Linear Algebra and Its Applications, 194:149–160, 1993.
- Cahit Arf, Untersuchungen über reinverzweigte Erweiterungen diskret bewerteter perfekter Körper, J. Reine Angew. Math. 181 (1939), 1–44 (German). MR 18, DOI 10.1515/crll.1940.181.1
- Frank Hansen, An operator inequality, Math. Ann. 246 (1979/80), no. 3, 249–250. MR 563403, DOI 10.1007/BF01371046
- Frank Hansen, Extrema for concave operator mappings, Math. Japon. 40 (1994), no. 2, 331–338. MR 1297250
- Frank Hansen and Gert Kjaergȧrd Pedersen, Jensen’s inequality for operators and Löwner’s theorem, Math. Ann. 258 (1981/82), no. 3, 229–241. MR 649196, DOI 10.1007/BF01450679
- F. Hartogs, Zur Theorie der analytischen Funktionen mehrerer unabhängiger Veränderlichen, inbesonderere über die Darstellung derselben durch Reihen, welche nach Potenzen einer Veränderlichen fortschreiten, Math. Ann., 62:1–88, 1906.
- R.V. Kadison and J.R. Ringrose, Fundamentals of the Theory of Operator Algebras, I-II, Academic Press, 1982 & 1986.
- Adam Korányi, On some classes of analytic functions of several variables, Trans. Amer. Math. Soc. 101 (1961), 520–554. MR 136765, DOI 10.1090/S0002-9947-1961-0136765-6
- F. Kraus, Über konvekse Matrixfunktionen, Math. Z., 41:18–42, 1936.
- K. Löwner, Über monotone Matrixfunktionen, Math. Z., 38:177–216, 1934.
- Harkrishan Vasudeva, On monotone matrix functions of two variables, Trans. Amer. Math. Soc. 176 (1973), 305–318. MR 313855, DOI 10.1090/S0002-9947-1973-0313855-4
Additional Information
- Frank Hansen
- Affiliation: Institute of Economics, University of Copenhagen, Studiestraede 6, DK-1455 Copenhagen K, Denmark
- ORCID: 0000-0003-3701-4214
- Received by editor(s): February 2, 1996
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2093-2102
- MSC (1991): Primary 47A63; Secondary 47A80, 47Bxx
- DOI: https://doi.org/10.1090/S0002-9939-97-04003-3
- MathSciNet review: 1416088