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 $C^{\ast }$-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