Tracial approximation is stable

Elliott, George; Fan, Qingzhai

doi:10.1090/proc/13601

Tracial approximation is stable
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by George A. Elliott and Qingzhai Fan PDF

Proc. Amer. Math. Soc. 145 (2017), 3877-3885 Request permission

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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