Quasidiagonal $C^\ast$-algebras and Nonstandard Analysis
Operator Algebras
2007-05-23 v2 Logic
Abstract
Suppose B is an ultraproduct of finite dimensional C^\ast-algebras. We consider mapping and injectability properties for separable C^\ast-algebras into B. In the case of approximately finite C^\ast-algebras, we obtain a classification of these mappings up to inner conjugacy. Using a Theorem of Voiculescu, we show that for nuclear C^\ast-algebras injectability into an ultraproduct of finite dimensional C^\ast-algebras is equivalent to quasidiagonality.
Cite
@article{arxiv.math/0209292,
title = {Quasidiagonal $C^\ast$-algebras and Nonstandard Analysis},
author = {F. Javier Thayer},
journal= {arXiv preprint arXiv:math/0209292},
year = {2007}
}
Comments
18 pages Revised introduction, bibliography. Added other corrections