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

F. Javier Thayer
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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.

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F. Javier Thayer. 2002-12-13. Quasidiagonal $C^\ast$-algebras and Nonstandard Analysis. https://arxiv.org/abs/math/0209292

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