Simple corona $C^*$-algebras
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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.References
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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
- Received by editor(s): February 1, 2003
- Published electronically: June 16, 2004
- Additional Notes: This research was partially supported by NSF grant DMS 0097003
- Communicated by: David R. Larson
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3215-3224
- MSC (2000): Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-04-07607-5
- MathSciNet review: 2073295