Type II₁ factors satisfying the spatial isomorphism conjecture

Cameron, J., Christensen, E., Sinclair, A.M., Smith, R.R., White, S.A. and Wiggins, A.D. (2012) Type II₁ factors satisfying the spatial isomorphism conjecture. Proceedings of the National Academy of Sciences of the United States of America, 109(50), pp. 20338-20343. (doi: 10.1073/pnas.1217792109)

Abstract

This paper addresses a conjecture in the work by Kadison and Kastler [Kadison RV, Kastler D (1972) Am J Math 94:38–54] that a von Neumann algebra M on a Hilbert space H should be unitarily equivalent to each sufficiently close von Neumann algebra N, and, moreover, the implementing unitary can be chosen to be close to the identity operator. This conjecture is known to be true for amenable von Neumann algebras, and in this paper, we describe classes of nonamenable factors for which the conjecture is valid. These classes are based on tensor products of the hyperfinite II₁ factor with crossed products of abelian algebras by suitably chosen discrete groups.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: White, Professor Stuart
• Authors: Cameron, J., Christensen, E., Sinclair, A.M., Smith, R.R., White, S.A., and Wiggins, A.D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Proceedings of the National Academy of Sciences of the United States of America
• Publisher: National Academy of Sciences of the United States of America
• ISSN: 0027-8424
• ISSN (Online): 1091-6490
• Published Online: 26 November 2012
• Copyright Holders: Copyright © 2012 National Academy of Sciences of the United States of America
• First Published: First published in Proceedings of the National Academy of Sciences of the United States of America 109(50):20338-20343
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
59641	1	The Cuntz Semigroup and the Fine Structure of Nuclear C*-Algebras	Stuart White	Engineering & Physical Sciences Research Council (EPSRC)	EP/I019227/1	M&S - MATHEMATICS