Invariant subspace lattices and kernel maps
We introduce the concept of the kernel map of an operator relative to a subspace lattice, outlining some of its properties and applications. In particular, we use these maps to show that any finite rank operator in a norm closed Lie module of a continuous nest algebra can be decomposed as a sum of finitely many rank-1 operators in the module. The hypothesis of the continuity of the nest cannot be dropped, in general.
The talk is based on joint work with Gabriel Matos.