  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.

Functional Analysis;Operator Algebras