Hochschild cohomology of factors with property Γ

• 成果类型: Article
• 署名作者: Christensen, E; Pop, F; Sinclair, AM; Smith, RR
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2003.158.635
• 发表日期: 2003
• 页码: 635-659
• 关键词: von-neumann-algebras; operator algebras; cartan subalgebras; banach algebras; derivations; ii1; perturbations; SEQUENCES; entropy; index

摘要

The main result of this paper is that the k(th) continuous Hochschild cohomology groups H-k(M,M) and Hk(M,B(H)) of a von Neumann factor M subset of or equal to B(H) of type 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 parallel to . parallel to(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.