文章基本信息

标题：Property Γ factors and the Hochschild cohomology problem
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作者：Erik Christensen ; Florin Pop ; Allan M. Sinclair 等
期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2003
卷号：100
期号：7
页码：3865-3869
DOI：10.1073/pnas.0737489100
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：The main result of this article is that the kth continuous Hochschild cohomology groups Hk([M], [M]) and Hk([M], B(H)) of a von Neumann factor [M] {subseteq} B(H) of type II1 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 ||*||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.