Voiculescu's theorem for nonseparable -algebras

Andrea Vaccaro

doi:10.1017/jsl.2020.22

Voiculescu's theorem for nonseparable -algebras

Andrea Vaccaro

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We prove that Voiculescu's noncommutative version of the Weyl-von Neumann Theorem can be extended to all unital, separably representable -algebras whose density character is strictly smaller than the (uncountable) cardinal invariant. We show moreover that Voiculescu's Theorem consistently fails for -algebras of larger density character.

Original language	English
Pages (from-to)	624-631
Number of pages	8
Journal	Journal of Symbolic Logic
Volume	85
Issue number	2
DOIs	https://doi.org/10.1017/jsl.2020.22
State	Published - 1 Jun 2020

Keywords

Martin’s Axiom
Voiculescu’s Theorem
nonseparable C*-algebras

ASJC Scopus subject areas

Philosophy
Logic

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10.1017/jsl.2020.22

Cite this

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title = "Voiculescu's theorem for nonseparable -algebras",

abstract = "We prove that Voiculescu's noncommutative version of the Weyl-von Neumann Theorem can be extended to all unital, separably representable -algebras whose density character is strictly smaller than the (uncountable) cardinal invariant. We show moreover that Voiculescu's Theorem consistently fails for -algebras of larger density character.",

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AB - We prove that Voiculescu's noncommutative version of the Weyl-von Neumann Theorem can be extended to all unital, separably representable -algebras whose density character is strictly smaller than the (uncountable) cardinal invariant. We show moreover that Voiculescu's Theorem consistently fails for -algebras of larger density character.

KW - Martin’s Axiom

KW - Voiculescu’s Theorem

KW - nonseparable C-algebras

UR - https://www.scopus.com/pages/publications/85100134922

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DO - 10.1017/jsl.2020.22

M3 - Article

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EP - 631

JO - Journal of Symbolic Logic

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IS - 2

ER -

Voiculescu's theorem for nonseparable -algebras

Abstract

Keywords

ASJC Scopus subject areas

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