The Fredholm Radius of a Bundle of Closed Linear Operators
E.-O. Liebetrau · Proceedings of the American Mathematical Society · 1978
Given a bundle of linear operators $T - \lambda S$, where T is closed and S is bounded, a sequence $\{ {\delta _m}(T:S)\}$ of extended real numbers is defined. If T is a Fredholm operator, the limit ${\lim \delta _m}{(T:S)^{1/m}}$ exists and is equal to the supremum of all $r > 0$ such that $T - \lambda S$ is a Fredholm operator for $|\lambda | < r$.