Vol. 288, No. 1, 2017

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ISSN: 0030-8730
A new bicommutant theorem

Ilijas Farah

Vol. 288 (2017), No. 1, 69–85
DOI: 10.2140/pjm.2017.288.69
Abstract

We prove an analogue of Voiculescu’s theorem: the relative bicommutant of a separable unital subalgebra A of an ultraproduct of simple unital C-algebras is equal to A.

Keywords
C*-algebras, ultrapowers, relative commutant, bicommutant
Mathematical Subject Classification 2010
Primary: 03C20, 03C98, 46L05
Milestones
Received: 13 May 2016
Revised: 20 September 2016
Accepted: 22 September 2016
Published: 8 April 2017
Authors
Ilijas Farah
Department of Mathematics and Statistics
York University
4700 Keele Street
Toronto, ON M3J1P3
Canada