Locally pre-$C$*-equivalent algebras
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Abstract:
We prove a weaker form of Cuntz’s theorem: every locally pre-$C^*$-equivalent Banach *-algebra is $C^*$-equivalent. Using this result, we obtain local conditions for the existence of an equivalent $C^*$-norm.References
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Additional Information
- Wei Wu
- Affiliation: Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China
- Email: wwu@math.ecnu.edu.cn
- Received by editor(s): September 27, 2001
- Published electronically: June 3, 2002
- Additional Notes: The author was supported in part by Shanghai Priority Academic Discipline
- Communicated by: David R. Larson
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 555-562
- MSC (2000): Primary 46K10
- DOI: https://doi.org/10.1090/S0002-9939-02-06686-8
- MathSciNet review: 1933347