  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.
