Remarks on the continuous L^2-cohomology of von Neumann algebras

Details Remarks on the continuous L^2-cohomology of von Neumann algebras Remarks on the continuous L^2-cohomology of von Neumann algebras

2011-10-27

arxiv.org/abs/1110.6155v1

Mathematics

Operator Algebras

11 pages

Scientific paper

We prove that norm continuous derivations from a von Neumann algebra into the algebra of operators affiliated with its tensor square are automatically continuous for the strong operator topology as well. From this we rederive previously known computational results regarding the first continuous L^2-Betti number for von Neumann algebras, and furthermore prove that it vanishes whenever the von Neumann algebra in question is a property (T) factor.

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