Illinois Journal of Mathematics

Tracially quasidiagonal extensions and topological stable rank

Huaxin Lin and Hiroyuki Osaka

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138201

Digital Object Identifier
doi:10.1215/ijm/1258138201

Mathematical Reviews number (MathSciNet)
MR2007244

Zentralblatt MATH identifier
1030.46076

Subjects
Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46L35: Classifications of $C^*$-algebras 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]

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


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