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arXiv · 1609.01093

Finite approximation properties of $C^{*}$-modules

Massoud Amini
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Abstract

We study the notions of nuclearity and exactness for module maps on $C^{*}$-algebras which are $C^*$-module over another $C^*$-algebra with compatible actions and examine finite approximation properties of such $C^*$-modules. We prove module versions of the results of Kirchberg and Choi-Effros. As a concrete example we extend the finite dimensional approximation properties of reduced $C^*$-algebras and von Neumann algebras on countable discrete groups to these operator algebras on countable inverse semigroups with the module structure coming from the action of the $C^*$-algebras on the subsemigroup of idempotents.

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Massoud Amini. 2016-09-05. Finite approximation properties of $C^{*}$-modules. https://arxiv.org/abs/1609.01093

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