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Tracial approximation is stable


Authors: George A. Elliott and Qingzhai Fan
Journal: Proc. Amer. Math. Soc. 145 (2017), 3877-3885
MSC (2010): Primary 46L35, 46L05, 46L80
DOI: https://doi.org/10.1090/proc/13601
Published electronically: February 22, 2017
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Abstract: Let $ \Omega $ be a class of unital C$ ^*$-algebras such that $ \Omega $ is closed under tensoring with matrix algebras and taking unital hereditary C$ ^*$-subalgebras and such that $ tsr(B)=1$ and the Cuntz semigroup Cu$ (B)$ is almost unperforated for any $ B\in \Omega $. Then $ A\in $ TA$ \Omega $ for any unital C$ ^*$-algebra $ A\in $ TA(TA$ \Omega )$. As an application, this result can be used to study tracially quasidiagonal C$ ^*$-algebra extensions of tracial topological rank no more than one.


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Additional Information

George A. Elliott
Affiliation: Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4C
Email: elliott@math.toronto.edu

Qingzhai Fan
Affiliation: Department of Mathematics, Shanghai Maritime University, Shanghai, People’s Republic of China 201306
Email: fanqingzhai@fudan.edu.cn, qzfan@shmtu.edu.cn

DOI: https://doi.org/10.1090/proc/13601
Keywords: C$^*$-algebras, tracial approximation, Cuntz semigroup
Received by editor(s): February 28, 2016
Received by editor(s) in revised form: September 21, 2016
Published electronically: February 22, 2017
Communicated by: Adrian Ioana
Article copyright: © Copyright 2017 American Mathematical Society