Notes on Rank-One Perturbed Resolvent

Details Notes on Rank-One Perturbed Resolvent Notes on Rank-One Perturbed Resolvent

2003-12-05

arxiv.org/abs/math-ph/0312016v3

Physics

Mathematical Physics

Latex 2.09, one misprint corrected

Scientific paper

This paper is a didactic comment (a transcription with variations) to the paper of S.R. Foguel {\it Finite Dimensional Perturbations in Banach Spaces}. Addressed, mainly: postgraduates and related readers. Subject: Suppose we have two linear operators, T_1, T_2, so that T_2^{-1} - T_1^{-1} is rank-one. What we want to know is how we can express (z-T_2)^{-1} in terms of T_2^{-1} - T_1^{-1} and (z-T_1)^{-1} . Keywords: M.G.Krein's Formula, Finite Rank Perturbations.

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