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VOICULESCU’S THEOREM FOR NONSEPARABLE $\text{C}^{\ast} $-ALGEBRAS

Part of: Set theory Selfadjoint operator algebras

Published online by Cambridge University Press:  20 July 2020

ANDREA VACCARO
ANDREA VACCARO*
Affiliation:
DEPARTMENT OF MATHEMATICS BEN-GURION UNIVERSITY OF THE NEGEV P.O.B. 653, BE’ER SHEVA84105, ISRAELE-mail: vaccaro@post.bgu.ac.ilURL: http://www.math.wisc.edu/~lempp/
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Abstract

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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.

Keywords

Voiculescu’s Theoremnonseparable C*-algebrasMartin’s Axiom

MSC classification

Primary: 03E75: Applications of set theory
Secondary: 46L05: General theory of $C^*$-algebras 03E35: Consistency and independence results 03E50: Continuum hypothesis and Martin's axiom
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 2 , June 2020 , pp. 624 - 631
Creative Commons
Creative Common License - CCCreative Common License - BY
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

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