Voiculescu's Theorem for Nonseparable C*-algebras

TL;DR

This paper extends Voiculescu's noncommutative Weyl-von Neumann theorem to a broader class of nonseparable C*-algebras with density character below a certain cardinal, and discusses limitations of this extension.

Contribution

It proves the extension of Voiculescu's theorem to nonseparable C*-algebras with density character less than , and shows that such a generalization does not hold for larger density characters.

Findings

Extension of Voiculescu's theorem to certain nonseparable C*-algebras

Limitations of the theorem's generalization to larger density characters

Consistency results regarding the theorem's applicability

Abstract

We prove that Voiculescu's noncommutative version of the Weyl-von Neumann theorem can be extended to all (not necessarily separable) unital, separably representable C*-algebras whose density character is strictly smaller than $\mathfrak{p}$. We show moreover that Voiculescu's theorem consistently does not generalize to C*-algebras of larger density character.