Kernel maps and operator decomposition

Abstract

We introduce the notions of kernel map and kernel set of a bounded linear operator on a Hilbert space relative to a subspace lattice. The characterization of the kernel maps and kernel sets of finite rank operators leads to showing that every norm closed Lie module of a continuous nest algebra is decomposable. The continuity of the nest cannot be lifted, in general.

This new version has minor changes relative to v1. The final version will be published in the Banach J. Math. Anal