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Simple corona $C^*$-algebras

Author(s): Huaxin Lin
Journal: Proc. Amer. Math. Soc. 132 (2004), 3215-3224.
MSC (2000): Primary 46L05
Posted: June 16, 2004
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Abstract: Let $A$ be a non-unital and $\sigma$-unital simple $C^*$-algebra. We show that if $M(A)/A$ is simple, then $M(A)/A$ is purely infinite. We also show that $M(A)/A$ is simple if and only if $A$ has a continuous scale provided that $A$ is not isomorphic to ${\mathcal K},$ the compact operators.

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Additional Information:

Huaxin Lin
Affiliation: Department of Mathematics, East China Normal University, Shanghai, China
Address at time of publication: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222

DOI: 10.1090/S0002-9939-04-07607-5
PII: S 0002-9939(04)07607-5
Keywords: Simple $C^*$-algebras, corona algebras
Received by editor(s): February 1, 2003
Posted: June 16, 2004
Additional Notes: This research was partially supported by NSF grant DMS 0097003
Communicated by: David R. Larson
Copyright of article: Copyright 2004, American Mathematical Society

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