Bimodules of Nest Subalgebras of von Neumann Algebras

The σ-weakly closed bimodules of nest subalgebras of σ-finite factor von Neumann algebras are characterized and structurally analysed. This generalizes work accomplished earlier by Erdos and Power for the case in which the factor is B ( H ). In the general case many more such bimodules exist than are given by a straightforward extension of the B ( H ) theory. New techniques are developed for this, including use of a partial coordinate system for bimodules, and a structural analysis of a certain boundary subspace affiliated with a lattice homomorphism of a nest.