title: Property gamma factors and the Hochschild cohomology problem.
abstract: The main result of this article is that the kth continuous Hochschild cohomology groups H(k)(M,M ) and H(k)(M, B(H)) of a von Neumann factor subset, dbl equals B(H) of type II(1) with property Gamma are 0 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 parallel. parallel (2) norm of separately ultraweakly continuous multilinear maps and combine these results to reduce to the case of completely bounded cohomology, which is already solved.
authors.affiliation: Institute for Mathematiske Fag, University of Copenhagen, Universitetsparken 5, DK 2100 Copenhagen, Denmark.
authors.forename: Erik
authors.initials: E
authors.lastname: Christensen
authors.forename: Florin
authors.initials: F
authors.lastname: Pop
authors.forename: Allan M
authors.initials: AM
authors.lastname: Sinclair
authors.forename: Roger R
authors.initials: RR
authors.lastname: Smith