Invariant subspaces for positive operators on Banach spaces with unconditional basis
Functional Analysis
2020-05-05 v1
Abstract
We prove that every lattice homomorphism acting on a Banach space with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal, which is no longer true for every positive operator on such a space. Motivated by these later examples, we characterize tridiagonal positive operators without non-trivial closed invariant ideals on extending to this context a result of Grivaux on the existence of non-trivial closed invariant subspaces for tridiagonal operators.
Cite
@article{arxiv.2005.01150,
title = {Invariant subspaces for positive operators on Banach spaces with unconditional basis},
author = {Eva A. Gallardo-Gutiérrez and Javier González-Doña and Pedro Tradacete},
journal= {arXiv preprint arXiv:2005.01150},
year = {2020}
}