## Illinois Journal of Mathematics

### Tracially quasidiagonal extensions and topological stable rank

#### 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.

#### Article information

Source
Illinois J. Math., Volume 47, Number 3 (2003), 921-937.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138201

Digital Object Identifier
doi:10.1215/ijm/1258138201

Mathematical Reviews number (MathSciNet)
MR2007244

Zentralblatt MATH identifier
1030.46076

#### Citation

Lin, Huaxin; Osaka, Hiroyuki. Tracially quasidiagonal extensions and topological stable rank. Illinois J. Math. 47 (2003), no. 3, 921--937. doi:10.1215/ijm/1258138201. https://projecteuclid.org/euclid.ijm/1258138201