Abstract
Let $0\rightarrow I\rightarrow A\rightarrow A/I \rightarrow 0$ be a short exact sequence of $C^*$-algebras with $A$ unital. Suppose that $I$ has tracial topological rank no more than one and $A/I$ is TAI (in particular, if $A/I$ is simple and has tracial topological rank no more than one). It will be proved that $A$ has tracial topological rank no more than one if the extension is quasidiagonal, and $A$ has the property ($P_1$) if the extension is tracially quasidiagonal.
Citation
Xiaochun Fang. Yile Zhao. "The extensions of $C^*$-algebras with tracial topological rank no more than one." Illinois J. Math. 53 (2) 441 - 462, Summer 2009. https://doi.org/10.1215/ijm/1266934787
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