Further extension

of the Heinz-Kato-Furuta inequality

Author:
Mitsuru Uchiyama

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2899-2904

MSC (1991):
Primary 47A63, 47A30, 47B25

Published electronically:
April 23, 1999

MathSciNet review:
1654068

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a bounded operator on a Hilbert space and positive definite operators. Kato has shown that if and for all , then where are operator monotone functions defined on such that . Furuta has shown that Let be any continuous operator monotone functions, and set for We will show that is well defined and Moreover, we will extend this result for unbounded closed operators densely defined on

**1.**Takayuki Furuta,*An extension of the Heinz-Kato theorem*, Proc. Amer. Math. Soc.**120**(1994), no. 3, 785–787. MR**1169027**, 10.1090/S0002-9939-1994-1169027-6**2.**Erhard Heinz,*Beiträge zur Störungstheorie der Spektralzerlegung*, Math. Ann.**123**(1951), 415–438 (German). MR**0044747****3.**Tosio Kato,*Notes on some inequalities for linear operators*, Math. Ann.**125**(1952), 208–212. MR**0053390****4.**K. Löwner,*Über monotone Matrixfunktionen*, Math. Z.**38**(1934), 177 - 216.**5.**Marvin Rosenblum and James Rovnyak,*Hardy classes and operator theory*, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1985. Oxford Science Publications. MR**822228**

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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:
http://dx.doi.org/10.1090/S0002-9939-99-05266-1

Keywords:
L\"{o}wner theory,
Heinz inequality,
operator monotone function,
closed operator,
non-negative operator

Received by editor(s):
June 6, 1997

Received by editor(s) in revised form:
December 9, 1997

Published electronically:
April 23, 1999

Additional Notes:
This research was partially supported by Grant-in-Aid for Scientific Research.

Communicated by:
David R. Larson

Article copyright:
© Copyright 1999
American Mathematical Society