| Given two von Neumann algebras M and N acting on the same Hilbert space, d(M,N) is defined to be the Hausdor 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, alpha is a free action of G on P 0 and N is a von Neumann algebra such that d(N, P0 x|alpha G) < 1/7 · 10--7, then N and P0 x| 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. |
