STABLE EQUIVALENCE OF THE WEAK CLOSURES OF FREE GROUPS CONVOLUTION-ALGEBRAS

We prove in this paper that the von Neumann algebras associated to the free non-commutative groups are stably isomorphic, i.e. that they are isomorphic when tensorized by the algebra of all linear bounded opera tors on a separable, infinite dimensional Hilbert space. This gives po sitive evidence for an old question, due to R.V. Kadison (see also S. Sakai's book on W-algebras). whether the von Neumann algebras associa ted to free groups are isomorphic or not.