Almost commuting unitaries and classification of purely infinite simple \(C^*\)-algebras
The author proves some results on approximating pairs of almost commuting unitaries by commuting unitaries. These are applied to show, e.g., that \[ {\mathcal A}_\theta\otimes{\mathcal O}_2\cong\ell_2 \quad\text{and}\quad {\mathcal B}_\theta\otimes{\mathcal O}_2\cong{\mathcal O}_2, \] where \({\mathcal A}_\theta\) and \({\mathcal B}_\theta\) are an irrational rotation algebra and a Bunce-Deddens algebra, respectively. These special results originally obtained in 1993 are now superseded by the work of E. Kirchberg and N. C. Philipps (1997).
classification of purely infinite simple \(C^\ast\)-algebras
scientific article; zbMATH DE number 1199743
scientific article