Type II_1 factors satisfying the spatial isomorphism conjecture
Operator Algebras
2013-07-30 v1
Abstract
This paper addresses a conjecture of Kadison and Kastler 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 is known to be true for amenable von Neumann algebras and in this paper we describe new classes of non-amenable factors for which the conjecture is valid. These are based on tensor products of the hyperfinite II_1 factor with crossed products of abelian algebras by suitably chosen discrete groups.
Cite
@article{arxiv.1211.6963,
title = {Type II_1 factors satisfying the spatial isomorphism conjecture},
author = {Jan Cameron and Erik Christensen and Allan M. Sinclair and Roger R. Smith and Stuart White and Alan D. Wiggins},
journal= {arXiv preprint arXiv:1211.6963},
year = {2013}
}
Comments
12 Pages. This is a shorter, expository version of arXiv:1209.4116, containing heuristic arguments and some sketch proofs