Abstract
We classify thewot-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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.