Abstract
It is known that a unital simple $C^*$-algebra $A$ with tracial topological rank zero has real rank zero and topological stable rank one. In this note we construct unital $C^*$-algebras with tracial topological rank zero but topological stable rank two.
Citation
Huaxin Lin. Hiroyuki Osaka. "Tracially quasidiagonal extensions and topological stable rank." Illinois J. Math. 47 (3) 921 - 937, Fall 2003. https://doi.org/10.1215/ijm/1258138201
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