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VOICULESCU’S THEOREM FOR NONSEPARABLE
$\text{C}^{\ast} $-ALGEBRAS
Published online by Cambridge University Press: 20 July 2020
Abstract
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.
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- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Copyright
- © The Author(s), 2020. Published by Cambridge University Press
References
REFERENCES
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