An Affirmative Answer to a Core Issue on Limit Operators
Functional Analysis
2015-11-23 v2 Operator Algebras
Abstract
An operator on an -space is called band-dominated if it can be approximated, in the operator norm, by operators with a banded matrix representation. It is known that a rich band-dominated operator is -Fredholm (which is a generalization of the classical Fredholm property) if and only if all of its so-called limit operators are invertible and their inverses are uniformly bounded. We show that the condition on uniform boundedness is redundant in this statement.
Cite
@article{arxiv.1401.1300,
title = {An Affirmative Answer to a Core Issue on Limit Operators},
author = {Marko Lindner and Markus Seidel},
journal= {arXiv preprint arXiv:1401.1300},
year = {2015}
}