Hochschild Cohomology of Factors with Property Γ

2001/07/31 by Erik Christensen, Florin Pop, Allan Sinclair +1
Mathematics · #math.OA #msc:46L05

paper · pdf

published as Ann. of Math. (2), vol. 158 (2003), no. 2, 635--659 · 25 pages, published version

arxiv created 2004/04/20 · arxiv updated 2009/11/30

Abstract

The main result of this paper is that the k^{\rm th} continuous Hochschild cohomology groups H^k(\cl M,\cl M) and H^k(\cl M,B(H)) of a von Neumann factor \cl M⊆ B(H) of type \rm II₁ with property Gamma 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 the case of completely bounded cohomology which is already solved.

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