The best possibility

of the grand Furuta inequality

Author:
Kôtarô Tanahashi

Journal:
Proc. Amer. Math. Soc. **128** (2000), 511-519

MSC (1991):
Primary 47B15

DOI:
https://doi.org/10.1090/S0002-9939-99-05261-2

Published electronically:
July 6, 1999

MathSciNet review:
1654088

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be invertible bounded linear operators on a Hilbert space satisfying , and let be real numbers satisfying Furuta showed that if , then . This inequality is called the grand Furuta inequality, which interpolates the Furuta inequality

and the Ando-Hiai inequality ( ).

In this paper, we show the grand Furuta inequality is best possible in the following sense: that is, if , then there exist invertible matrices with which do not satisfy .

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Additional Information

**Kôtarô Tanahashi**

Email:
tanahasi@tohoku-pharm.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-99-05261-2

Keywords:
The L\"owner-Heinz inequality,
the Furuta inequality,
the grand Furuta inequality

Received by editor(s):
September 27, 1997

Received by editor(s) in revised form:
March 31, 1998

Published electronically:
July 6, 1999

Communicated by:
David R. Larson

Article copyright:
© Copyright 1999
American Mathematical Society