Almost invariant half-spaces of algebras of operators
Functional Analysis
2009-09-21 v1 Operator Algebras
Abstract
Given a Banach space X and a bounded linear operator T on X, a subspace Y of X is almost invariant under T if TY is a subspace of Y+F for some finite-dimensional ``error'' F. In this paper, we study subspaces that are almost invariant under every operator in an algebra A of operators acting on X. We show that if A is norm closed then the dimensions of ``errors'' corresponding to operators in A must be uniformly bounded. Also, if A is generated by a finite number of commuting operators and has an almost invariant half-space (that is, a subspace with both infinite dimension and infinite codimension) then A has an invariant half-space.
Cite
@article{arxiv.0909.3491,
title = {Almost invariant half-spaces of algebras of operators},
author = {Alexey I. Popov},
journal= {arXiv preprint arXiv:0909.3491},
year = {2009}
}
Comments
14 pages