On an approximate automorphism on a $C^{*}$-algebra
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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.References
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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
- 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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 2051135