Kenneth R. Davidson - Principal bimodules of nest algebras

We classify the WOT-closed bimodules over a pair of nest algebras which are singly generated as algebraic and as norm-closed bimodules. The obstructions relate to the finite rank atoms. In particular, if both nest algebras have infinite multiplicity, then every WOT-closed bimodule is (algebraically) principal. Another important special case is the ideal of strictly upper triangular operators, which is always principal; and the generator is a sum of commutators. In general, every countably generated WOT-closed bimodule is singly generated, and we obtain explicit bounds on the number and norms of the terms in a factorization through the generator.