Notes on Rank-One Perturbed Resolvent
Abstract
This paper is a didactic comment (a transcription with variations) to the paper of S.R. Foguel Finite Dimensional Perturbations in Banach Spaces. Addressed, mainly: postgraduates and related readers. Subject: Suppose we have two linear operators, T1, T2, so that T2-1 - T1-1 is rank-one. What we want to know is how we can express (z-T2)-1 in terms of T2-1 - T1-1 and (z-T1)-1 . Keywords: M.G.Krein's Formula, Finite Rank Perturbations.
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