Type II₁ factors satisfying the spatial isomorphism conjecture

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 [Formula] should be unitarily equivalent to each sufficiently close von Neumann algebra N , and, moreover, the implementing unitary c...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2012-12, Vol.109 (50), p.20338-20343
Main Authors: Cameron, Jan, Christensen, Erik, Sinclair, Allan M, Smith, Roger R, White, Stuart A, Wiggins, Alan D
Format: Article
Language:English
Subjects:
Algebra
data analysis
Embeddings
Ergodic theory
Hilbert spaces
Mathematical theorems
Operator algebras
Physical Sciences
spatial data
Subalgebras
Unit ball
validity
Von Neumann algebra
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Summary: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 [Formula] 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 II ₁ factor with crossed products of abelian algebras by suitably chosen discrete groups.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.1217792109