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On an approximate automorphism on a $C^{*}$-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: It is shown that for an approximate algebra homomorphism $f : \mathcal{B} \rightarrow \mathcal{B}$ on a Banach $*$-algebra $\mathcal{B}$, there exists a unique algebra $*$-homomorphism $H : \mathcal{B} \rightarrow \mathcal{B}$ near the approximate algebra homomorphism. This is applied to show that for an approximate automorphism $f : \mathcal{A} \rightarrow \mathcal{A}$on a unital $C^{*}$-algebra $\mathcal{A}$, there exists a unique automorphism $\alpha : \mathcal{A} \rightarrow \mathcal{A}$ near the approximate automorphism. In fact, we show that the approximate automorphism $f : \mathcal{A} \rightarrow \mathcal{A}$ 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

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