Quasidiagonal $C^\ast$-algebras and Nonstandard Analysis

Details Quasidiagonal $C^\ast$-algebras and Nonstandard Analysis Quasidiagonal $C^\ast$-algebras and Nonstandard Analysis

2002-09-23

arxiv.org/abs/math/0209292v2

Mathematics

Operator Algebras

18 pages Revised introduction, bibliography. Added other corrections

Scientific paper

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.

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