Type II1 factors satisfying the spatial isomorphism conjecture.

Jan  Cameron; Erik Christensen; Allan M.  Sinclair; Roger R.  Smith; Stuart  White; Alan D.  Wiggins

Type II1 factors satisfying the spatial isomorphism conjecture.

Jan Cameron, Erik Christensen, Allan M. Sinclair, Roger R. Smith, Stuart White, Alan D. Wiggins

Department of Mathematical Sciences

3 Citations (Scopus)

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.

Translated title of the contribution	Type II1 faktorer som opfylder den rumlige isomorfi hypotese.
Original language	English
Journal	Proceedings of the National Academy of Sciences USA (PNAS)
Volume	109
Issue number	5
Pages (from-to)	20338 - 20343
Number of pages	6
ISSN	0027-8424
Publication status	Published - 11 Dec 2012

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title = "Type II1 factors satisfying the spatial isomorphism conjecture.",

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.",

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language = "English",

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pages = "20338 -- 20343",

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TY - JOUR

T1 - Type II1 factors satisfying the spatial isomorphism conjecture.

AU - Cameron, Jan

AU - Christensen, Erik

AU - Sinclair, Allan M.

AU - Smith, Roger R.

AU - White, Stuart

AU - Wiggins, Alan D.

PY - 2012/12/11

Y1 - 2012/12/11

N2 - 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.

AB - 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.

M3 - Journal article

SN - 0027-8424

VL - 109

SP - 20338

EP - 20343

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 5

ER -

Type II1 factors satisfying the spatial isomorphism conjecture.

Abstract

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