Approximated by finite-dimensional homomorphisms into simple 𝐶*-algebras with tracial rank one

Liu, Junping; Zhang, Yifan

doi:10.1090/S0002-9939-2014-12350-1

Approximated by finite-dimensional homomorphisms into simple $C^*$-algebras with tracial rank one
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by Junping Liu and Yifan Zhang PDF

Proc. Amer. Math. Soc. 142 (2014), 3941-3952 Request permission

Abstract:

We discuss when a unital homomorphism $\phi : C(X)\rightarrow A$ can be approximated by finite-dimensional homomorphisms, where $X$ is a compact metric space and $A$ is a unital simple $C^*$-algebra with tracial rank one. In this paper, we will give a necessary and sufficient condition.

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