PRINCIPAL BIMODULES OF NEST-ALGEBRAS

We classify the WOT-closed bimodules over a pair of nest algebras whic h are singly generated as algebraic and as norm-closed bimodules. The obstructions relate to the finite rank atoms. In particular, ii both n est algebras have infinite multiplicity, then every WOT-closed bimodul e is (algebraically) principal. Another important special case is the ideal of strictly upper triangular operators, which is always principa l; and the generator is a sum of commutators. In general, every counta bly generated wet-closed bimodule is singly generated, and we obtain e xplicit bounds on the number and nons of the terms in a factorization through the generator. (C) 1998 Academic Press.