Norm-closed bimodules of nest algebras. (English) Zbl 0994.47072
Summary: We study the support and essential support functions of a norm-closed bimodule of a nest algebra. An allowable support function pair determines a maximal bimodule. There is also a natural candidate for the minimal bimodule for a given support function pair. We determine precisely when this candidate is the minimal element. In the other cases, this module is still the intersection of all bimodules with a given support function pair, but it is not in this class itself.
MSC:
| 47L35 | Nest algebras, CSL algebras |
| 47C15 | Linear operators in \(C^*\)- or von Neumann algebras |
| 46H25 | Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) |
