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Locally pre-$C$*-equivalent algebras

Author(s): Wei Wu
Journal: Proc. Amer. Math. Soc. 131 (2003), 555-562.
MSC (2000): Primary 46K10
Posted: June 3, 2002
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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.

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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

DOI: 10.1090/S0002-9939-02-06686-8
PII: S 0002-9939(02)06686-8
Keywords: $C^*$-equivalent algebra, pre-$C^*$-equivalent, locally pre-$C^*$-equivalent
Received by editor(s): September 27, 2001
Posted: June 3, 2002
Additional Notes: The author was supported in part by Shanghai Priority Academic Discipline
Communicated by: David R. Larson
Copyright of article: Copyright 2002, American Mathematical Society

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