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arXiv · 1401.1300

An Affirmative Answer to a Core Issue on Limit Operators

Marko Lindner·Markus Seidel
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Abstract

An operator on an $l^{p}$-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 $\mathcal{P}$-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.

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Marko Lindner, Markus Seidel. 2014-01-07. An Affirmative Answer to a Core Issue on Limit Operators. https://doi.org/10.1016/j.jfa.2014.03.002

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