Ideals of multiplier algebras of simple AF 𝐶*-algebras

Lin, Hua Xin

doi:10.1090/S0002-9939-1988-0958075-1

Ideals of multiplier algebras of simple AF $C^ *$-algebras
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Proc. Amer. Math. Soc. 104 (1988), 239-244 Request permission

Abstract:

It is shown that the ${C^ * }$-algebra $M(A)/A$, where $A$ is a nonunital separable simple AF ${C^ * }$-algebra and $M(A)$ is the multiplier algebra of $A$, is simple if and only if $A$ has a continuous scale or $A$ is elementary. Some results concerning the ideal structure of $M(A)/A$ are also obtained in the case that it is nontrivial.

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