The Furuta inequality with negative powers

Author:
Kôtarô Tanahashi

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1683-1692

MSC (1991):
Primary 47B15

DOI:
https://doi.org/10.1090/S0002-9939-99-04705-X

Published electronically:
February 11, 1999

MathSciNet review:
1476395

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be bounded linear operators on a Hilbert space satisfying . Furuta showed the operator inequality

as long as positive real numbers satisfy and . In this paper, we show this inequality is valid if negative real numbers satisfy a certain condition. Also, we investigate the optimality of that condition.

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Additional Information

**Kôtarô Tanahashi**

Affiliation:
Department of Mathematics, Tohoku College of Pharmacy, Komatsushima, Aoba-ku, Sendai 981, Japan

Email:
tanahasi@tohoku-pharm.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-99-04705-X

Keywords:
L\"{o}wner-Heinz inequality,
the Furuta inequality,
positive operator

Received by editor(s):
September 29, 1995

Received by editor(s) in revised form:
June 12, 1996, August 6, 1996, October 23, 1996, April 3, 1997, and September 4, 1997

Published electronically:
February 11, 1999

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1999
American Mathematical Society