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 ⊆ B(H) of type II1 with property Γ 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.
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机译：本文的主要结果是冯·诺依曼的第k个连续的Hochschild同调群H k （ℳ，ℳ）和H k （ℳ，B（H））对于所有正整数k，具有属性Γ的II1类型的因子⊆B（H）均为0。证明方法涉及构造具有特殊性质的超有限子因子以及用于多线性映射的Grothendieck类型的新不等式。我们证明了分别在超弱连续多线性映射的∥⋅∥2范数中的联合连续性，并将这些结果组合起来，可以简化为完全有界同调的情况，该问题已经解决。
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