A note on the Jensen inequality for self-adjoint operators
Tomohiro HAYASHI
Source: J. Math. Soc. Japan Volume 62, Number 3
(2010), 949-961.
Abstract
In this paper we consider a certain order-like relation for self-adjoint operators on a Hilbert space. This relation is defined by using the Jensen inequality. We will show that under some assumptions this relation is antisymmetric.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1280496825
Digital Object Identifier: doi:10.2969/jmsj/06230949
Zentralblatt MATH identifier: 05786476
Mathematical Reviews number (MathSciNet): MR2648068
References
T. Ando, Functional calculus with operator-monotone functions, Math. Inequal. Appl., to appear.
Mathematical Reviews (MathSciNet): MR2662014
J-C. Bourin, private communication.
J. B. Conway, A Course in Operator Theory, Graduate Studies in Mathematics, 21, American Mathematical Society, Providence, RI, 2000.
Mathematical Reviews (MathSciNet): MR1721402
Zentralblatt MATH: 0936.47001
T. Hayashi, Non-commutative arithmetic-geometric mean inequality, Proc. Amer. Math. Soc., 137 (2009), 3399–3406.
Mathematical Reviews (MathSciNet): MR2515409
Zentralblatt MATH: 1177.47023
Digital Object Identifier: doi:10.1090/S0002-9939-09-09911-0
Journal of the Mathematical Society of Japan
