Simple 𝐶*-algebras with continuous scales and simple corona algebras

Lin, Hua Xin

doi:10.1090/S0002-9939-1991-1079711-8

Simple $C^ *$-algebras with continuous scales and simple corona algebras
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Proc. Amer. Math. Soc. 112 (1991), 871-880 Request permission

Abstract:

It is shown that the corona algebra $M\left ( A \right )/A$ of a separable simple ${C^ * }$-algebra $A$ is simple if and only if $A$ has a continuous scale or $A$ is elementary. It is also shown that simple ${C^ * }$-algebras with continuous scales are algebraically simple.

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-algebras with real rank zero and internal structure of their corona and multiplier algebras