Perturbations of certain crossed product algebras by free groups

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 P-0 is an injective von Neumann algebra with a cyclic tracial vector, G is a free group, a is a free action of G on P-0 and N is a von Neumann algebra such that d(N, P-0 (sic)(alpha) G) < 1/7 X 10(-7), then N and P-0 unknown symble alpha G are spatially isomorphic. Suitable choices of the actions give the first examples of infinite noninjective factors for which this problem has a positive solution. (C) 2014 Elsevier Inc. All rights reserved.