Approximated by finite-dimensional homomorphisms into simple $C^*$-algebras with tracial rank one
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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.References
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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
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3251734