Fredholm Indices of Band-Dominated Operators

Abstract.

The Fredholmness of a band-dominated operator on $l^2 (\mathbb{Z})$ is closely related with the invertibility of its limit operators: the operator is Fredholm if and only if each of its limit operators is invertible and if the norms of their inverses are uniformly bounded. The goal of the present note is to show how the Fredholm index of a Fredholm band-dominated operator can be determined in terms of its limit operators.