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VOICULESCU’S THEOREM FOR NONSEPARABLE
$\text{C}^{\ast} $
-ALGEBRAS
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- Published online by Cambridge University Press:
- 20 July 2020, pp. 624-631
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We prove that Voiculescu’s noncommutative version of the Weyl-von Neumann Theorem can be extended to all unital, separably representable
$\mathrm {C}^\ast $
-algebras whose density character is strictly smaller than the (uncountable) cardinal invariant 
$\mathfrak {p}$
. We show moreover that Voiculescu’s Theorem consistently fails for 
$\mathrm {C}^\ast $
-algebras of larger density character.
