Dedicated to the memory of Barry Johnson, 1937–2002 Abstract The main result of this paper is that the k th continuous Hochschild cohomology groups H k (M, M) and H k (M, B(H)) of a von Neumann factor M ⊆ B(H) of type II1 with property Γ are zero for all positive integers k. The method of proof involves the construction of hyperfinite subfactors with special properties and a new inequality of Grothendieck type for multilinear maps. We prove joint continuity in the · 2 -norm of separately ultraweakly continuous multilinear maps, and combine these results to reduce to.
