On Generalized Resolvents
Constantin Apostol, Kevin F. Clancey · Proceedings of the American Mathematical Society · 1976
Let $T$ be a bounded linear operator on a Hilbert space and ${\rho _F}(T)$ the Fredholm domain of $T$. It is shown that a generalized resolvent can be constructed for $T$ in ${\rho _F}(T)$ which verifies the resolvent identity except for an at most countable set of points which are close to the boundary of ${\rho _F}(T)$.