**
Below is the ascii version of the abstract for 03-526.
The html version should be ready soon.**Sergej A. Choroszavin ( sergius@pve.vsu.ru )
Notes on Rank-One Perturbed Resolvent.
(18K, LaTeX 2.09)
ABSTRACT. 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 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} - (z-T_1)^{-1}
in terms of
T_1^{-1} \,,\, T_2^{-1}
(and, e.g.
(z-T_1)^{-1}
).
Keywords: M.G.Krein's Formula, Finite Rank Perturbations.