Almost invariant half-spaces of operators on Banach spaces
Functional Analysis
2009-01-08 v1
Abstract
We introduce and study the following modified version of the Invariant Subspace Problem: whether every operator T on a Banach space has an almost invariant half-space, that is, a subspace Y of infinite dimension and infinite codimension such that Y is of finite codimension in T(Y). We solve this problem in the affirmative for a large class of operators which includes quasinilpotent weighted shift operators on l_p (1 \le p < \infty) or c_0.
Keywords
Cite
@article{arxiv.0901.0752,
title = {Almost invariant half-spaces of operators on Banach spaces},
author = {George Androulakis and Alexey I. Popov and Adi Tcaciuc and Vladimir G. Troitsky},
journal= {arXiv preprint arXiv:0901.0752},
year = {2009}
}
Comments
13 pages