Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415099 | Journal of Functional Analysis | 2014 | 34 Pages |
Abstract
Given two von Neumann algebras M and N acting on the same Hilbert space, d(M,N) is defined to be the Hausdorff distance between their unit balls. The Kadison-Kastler problem asks whether two sufficiently close von Neumann algebras are spatially isomorphic. In this article, we show that if P0 is an injective von Neumann algebra with a cyclic tracial vector, G is a free group, α is a free action of G on P0 and N is a von Neumann algebra such that d(N,P0âαG)<1/7Ã10â7, then N and P0âαG are spatially isomorphic. Suitable choices of the actions give the first examples of infinite noninjective factors for which this problem has a positive solution.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Wai-Kit Chan,