On Semi-Fredholm Band-Dominated Operators

Abstract

In this paper we study the semi-Fredholm property of band-dominated operators $A$ and prove that it already implies the Fredholmness of $A$ in all cases where this is not disqualified by obvious reasons. Moreover, this observation is applied to show that the Fredholmness of a band-dominated operator already follows from the surjectivity of all its limit operators.

References in corpus (2)

• An Affirmative Answer to a Core Issue on Limit Operators
• Limit Operators, Collective Compactness, and the Spectral Theory of Infinite Matrices