Invariant half-spaces for rank-one perturbations
Functional Analysis
2020-06-19 v1
Abstract
If T is a bounded linear operator acting on an infinite-dimensional Banach space, then there exists and operator F of rank at most one and arbitrarily small norm such that T-F has an invariant subspace of infinite dimension and codimension. This improves results of Tcaciuc and other authors.
Cite
@article{arxiv.2006.10507,
title = {Invariant half-spaces for rank-one perturbations},
author = {Vladimir Muller},
journal= {arXiv preprint arXiv:2006.10507},
year = {2020}
}