Mean theoretic approach

to the grand Furuta inequality

Authors:
Masatoshi Fujii and Eizaburo Kamei

Journal:
Proc. Amer. Math. Soc. **124** (1996), 2751-2756

MSC (1991):
Primary 47A63, 47B15

DOI:
https://doi.org/10.1090/S0002-9939-96-03342-4

MathSciNet review:
1327013

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Abstract | References | Similar Articles | Additional Information

Abstract: Very recently, Furuta obtained the grand Furuta inequality which is a parameteric formula interpolating the Furuta inequality and the Ando-Hiai inequality as follows : If and is invertible, then for each ,

is a decreasing function of both and for all and . In this note, we employ a mean theoretic approach to the grand Furuta inequality. Consequently we propose a basic inequality, by which we present a simple proof of the grand Furuta inequality.

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Additional Information

**Masatoshi Fujii**

Affiliation:
Department of Mathematics, Osaka Kyoiku University, Asahigaoka, Kashiwara, Osaka 582, Japan

Email:
mfujii@cc.osaka-kyoiku.ac.jp

**Eizaburo Kamei**

Affiliation:
Momodani Senior Highschool, Ikuno, Osaka 544, Japan

DOI:
https://doi.org/10.1090/S0002-9939-96-03342-4

Keywords:
Positive operators,
L\"{o}wner-Heinz inequality,
Furuta inequality,
Ando-Hiai inequality,
grand Furuta inequality

Received by editor(s):
November 28, 1994

Received by editor(s) in revised form:
March 6, 1995

Dedicated:
Dedicated to Professor Tsuyoshi Ando, the originator of the theory of operator means, on his retirement from Hokkaido University

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1996
American Mathematical Society