On generalized resolvents

Apostol, Constantin; Clancey, Kevin

doi:10.1090/S0002-9939-1976-0410412-4

On generalized resolvents
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by Constantin Apostol and Kevin Clancey PDF

Proc. Amer. Math. Soc. 58 (1976), 163-168 Request permission

Abstract:

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 ${\rho _F}(T)$.

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