THE HOCHSCHILD COHOMOLOGY PROBLEM FOR VON-NEUMANN-ALGEBRAS

In 1967, when Kadison and Ringrose began the development of continuous cohomology theory for operator algebras, they conjectured that the co homology groups H-n(M, M), n greater than or equal to 1, for a von Neu mann algebra M, should all be zero, This conjecture, which has Importa nt structural implications for von Neumann algebras, has been solved a ffirmatively in the type I, II infinity, and III cases, leaving open o nly the type II1 case, In this paper, we describe a positive solution when M is type II1 and has a Cartan subalgebra and a separable predual .