An order characterization of commutativity for -algebras

Author:
Wei Wu

Journal:
Proc. Amer. Math. Soc. **129** (2001), 983-987

MSC (2000):
Primary 46L05

DOI:
https://doi.org/10.1090/S0002-9939-00-05724-5

Published electronically:
October 10, 2000

MathSciNet review:
1814137

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we investigate the problem of when a -algebra is commutative through operator-monotonic increasing functions. The principal result is that the function is operator-monotonic increasing on a -algebra if and only if is commutative. Therefore, -algebra is commutative if and only if in for all positive elements in .

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Additional Information

**Wei Wu**

Affiliation:
Institute of Mathematics, Academia Sinica, Beijing 100080, China

Address at time of publication:
Department of Mathematics, East China Normal University, Shanghai 200062, China

Email:
wwu@math03.math.ac.cn, wwu@math.ecnu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-00-05724-5

Keywords:
Commutativity for $C^{\ast }$-algebras,
operator-monotonic increasing function,
positive element

Received by editor(s):
November 4, 1998

Received by editor(s) in revised form:
June 4, 1999

Published electronically:
October 10, 2000

Communicated by:
David R. Larson

Article copyright:
© Copyright 2000
American Mathematical Society