SMOOTH BIMODULES AND COHOMOLOGY OF II<sub>1</sub> FACTORS
SMOOTH BIMODULES AND COHOMOLOGY OF II<sub>1</sub> FACTORS
We prove that, under rather general conditions, the 1-cohomology of a von Neumann algebra $M$ with values in a Banach $M$ -bimodule satisfying a combination of smoothness and operatorial conditions vanishes. For instance, we show that, if $M$ acts normally on a Hilbert space ${\mathcal{H}}$ and ${\mathcal{B}}_{0}\subset {\mathcal{B}}({\mathcal{H}})$ is a …