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


Authors: Junping Liu and Yifan Zhang
Journal: Proc. Amer. Math. Soc. 142 (2014), 3941-3952
MSC (2010): Primary 46L05, 46L35
DOI: https://doi.org/10.1090/S0002-9939-2014-12350-1
Published electronically: July 24, 2014
MathSciNet review: 3251734
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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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Additional Information

Junping Liu
Affiliation: Department of Mathematics, East China Normal University, Shanghai, People’s Republic of China
Email: jpliu@math.ecnu.edu.cn

Yifan Zhang
Affiliation: Department of Applied Mathematics, Xiamen University of Technology, Xiamen, People’s Republic of China
Email: yfzhang@xmut.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2014-12350-1
Keywords: Homomorphisms, tracial rank one
Received by editor(s): August 26, 2011
Received by editor(s) in revised form: September 12, 2012, and December 20, 2012
Published electronically: July 24, 2014
Additional Notes: This research was supported by the Research Center for Operator Algebras at ECNU, National Natural Science Foundation of China (Grant No. 10671068) and the National Natural Science Foundation of China (Grant No. 11171315).
Communicated by: Marius Junge
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.