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.