An operator inequality related to Jensen's inequality

Author:
Mitsuru Uchiyama

Journal:
Proc. Amer. Math. Soc. **129** (2001), 3339-3344

MSC (2000):
Primary 47A63, 15A48

DOI:
https://doi.org/10.1090/S0002-9939-01-06130-5

Published electronically:
April 9, 2001

MathSciNet review:
1845011

Full-text PDF

Abstract | References | Similar Articles | Additional Information

For bounded non-negative operators and , Furuta showed

We will extend this as follows: implies

where is a harmonic mean of and . The idea of the proof comes from Jensen's inequality for an operator convex function by Hansen-Pedersen.

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Additional Information

**Mitsuru Uchiyama**

Affiliation:
Department of Mathematics, Fukuoka University of Education, Munakata, Fukuoka, 811-4192, Japan

Email:
uchiyama@fukuoka-edu.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-01-06130-5

Keywords:
Order of selfadjoint operators,
Jensen inequality,
Furuta inequality

Received by editor(s):
March 21, 2000

Published electronically:
April 9, 2001

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2001
American Mathematical Society