Approximately unitarily equivalent morphisms and inductive limit \(C^*\)- algebras
Let \({\mathcal A}\) denote a simple \(C^*\)-algebra of real rank zero which is an inductive limit of homogeneous algebras whose spectra are finite CW complexes of uniformly bounded (or slowly growing) dimension and torsion free \(K^0\)-group. Using the Connes-Higson theory of asymptotic morphisms, the author shows that \({\mathcal A}\) falls into the class of simple \(C^*\)-algebras of real rank zero that are classified by their graded order-unit \(K\)-groups. This extends previous work by \textit{G. A. Elliott} [J. Reine Angew. Math. 443, 179-219 (1993; Zbl 0809.46067)] and Elliott and \textit{G. Gong} (to appear).
simple \(C^*\)-algebra of real rank zero
inductive limit of homogeneous algebras whose spectra are finite CW complexes
Connes-Higson theory of asymptotic morphisms
scientific article; zbMATH DE number 784416
scientific article