On an approximate automorphism on a -algebra

Author:
Chun-Gil Park

Journal:
Proc. Amer. Math. Soc. **132** (2004), 1739-1745

MSC (2000):
Primary 47B48, 46L40, 39B52

DOI:
https://doi.org/10.1090/S0002-9939-03-07252-6

Published electronically:
October 9, 2003

MathSciNet review:
2051135

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that for an approximate algebra homomorphism on a Banach -algebra , there exists a unique algebra -homomorphism near the approximate algebra homomorphism. This is applied to show that for an approximate automorphism on a unital -algebra , there exists a unique automorphism near the approximate automorphism. In fact, we show that the approximate automorphism is an automorphism.

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Additional Information

**Chun-Gil Park**

Affiliation:
Department of Mathematics, Chungnam National University, Daejeon 305-764, South Korea

Email:
cgpark@math.cnu.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-03-07252-6

Keywords:
Approximate algebra homomorphism,
approximate automorphism,
$C^{*}$-algebra,
stability,
functional equation

Received by editor(s):
December 2, 2002

Received by editor(s) in revised form:
February 3, 2003

Published electronically:
October 9, 2003

Additional Notes:
This work was supported by Korea Research Foundation Grant KRF-2002-041-C00014. The author would like to thank the referee for a number of valuable suggestions regarding a previous version of this paper

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2003
American Mathematical Society