Journal of the Mathematical Society of Japan

A note on the Jensen inequality for self-adjoint operators

Tomohiro HAYASHI

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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.

Article information

Source
J. Math. Soc. Japan, Volume 62, Number 3 (2010), 949-961.

Dates
First available in Project Euclid: 30 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1280496825

Digital Object Identifier
doi:10.2969/jmsj/06230949

Mathematical Reviews number (MathSciNet)
MR2648068

Zentralblatt MATH identifier
1216.47025

Subjects
Primary: 47A63: Operator inequalities

Keywords
operator inequality Jensen inequality

Citation

HAYASHI, Tomohiro. A note on the Jensen inequality for self-adjoint operators. J. Math. Soc. Japan 62 (2010), no. 3, 949--961. doi:10.2969/jmsj/06230949. https://projecteuclid.org/euclid.jmsj/1280496825


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References

  • T. Ando, Functional calculus with operator-monotone functions, Math. Inequal. Appl., to appear.
  • J-C. Bourin, private communication.
  • J. B. Conway, A Course in Operator Theory, Graduate Studies in Mathematics, 21, American Mathematical Society, Providence, RI, 2000.
  • T. Hayashi, Non-commutative arithmetic-geometric mean inequality, Proc. Amer. Math. Soc., 137 (2009), 3399–3406.