Simple corona 𝐶*-algebras

Lin, Huaxin

doi:10.1090/S0002-9939-04-07607-5

Simple corona $C^*$-algebras
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Proc. Amer. Math. Soc. 132 (2004), 3215-3224 Request permission

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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