Double relative commutants in coronas of separable C*-algebras

Dan Kucerovsky; Martin Mathieu

doi:10.1017/S0017089522000374

Double relative commutants in coronas of separable C*-algebras

Dan Kucerovsky^*, Martin Mathieu

^*Corresponding author for this work

School of Mathematics and Physics

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

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Abstract

We prove a double commutant theorem for separable subalgebras of a wide class of corona C*-algebras, largely resolving a problem posed by Pedersen in 1988. Double commutant theorems originated with von Neumann, whose seminal result evolved into an entire field now called von Neumann algebra theory. Voiculescu later proved a C*-algebraic double commutant theorem for subalgebras of the Calkin algebra. We prove a similar result for subalgebras of a much more general class of so-called corona C*-algebras.

Original language	English
Pages (from-to)	345-355
Number of pages	11
Journal	Glasgow Mathematical Journal
Volume	65
Issue number	2
Early online date	23 Nov 2022
DOIs	https://doi.org/10.1017/S0017089522000374
Publication status	Published - May 2023

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10.1017/S0017089522000374Licence: CC BY

Double relative commutants in coronas of separable C*-algebras
Copyright 2023 the authors. This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
Final published version, 262 KBLicence: CC BY

Cite this

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abstract = "We prove a double commutant theorem for separable subalgebras of a wide class of corona C*-algebras, largely resolving a problem posed by Pedersen in 1988. Double commutant theorems originated with von Neumann, whose seminal result evolved into an entire field now called von Neumann algebra theory. Voiculescu later proved a C*-algebraic double commutant theorem for subalgebras of the Calkin algebra. We prove a similar result for subalgebras of a much more general class of so-called corona C*-algebras.",

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AU - Mathieu, Martin

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DO - 10.1017/S0017089522000374

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JO - Glasgow Mathematical Journal

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Double relative commutants in coronas of separable C*-algebras

Abstract

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