Kernel maps and operator decomposition
Operator Algebras
2022-07-21 v2
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.
Cite
@article{arxiv.1902.07689,
title = {Kernel maps and operator decomposition},
author = {Gabriel Matos and Lina Oliveira},
journal= {arXiv preprint arXiv:1902.07689},
year = {2022}
}
Comments
This new version has minor changes relative to v1. The final version will be published in the Banach J. Math. Anal