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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Locally pre-$C$*-equivalent algebras


Author: Wei Wu
Journal: Proc. Amer. Math. Soc. 131 (2003), 555-562
MSC (2000): Primary 46K10
DOI: https://doi.org/10.1090/S0002-9939-02-06686-8
Published electronically: June 3, 2002
MathSciNet review: 1933347
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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

Keywords: $C^*$-equivalent algebra, pre-$C^*$-equivalent, locally pre-$C^*$-equivalent
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
Article copyright: © Copyright 2002 American Mathematical Society