**
Below is the ascii version of the abstract for 03-553.
The html version should be ready soon.**Sergej A. Choroszavin ( sergius@pve.vsu.ru )
Notes on Rank One Perturbed Resolvent.
Perturbation of Isolated Eigenvalue.
(24K, LaTeX 2.09)
ABSTRACT. This paper is a didactic commentary (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,
A, B,
so that
B - A is rank one.
Let \lambda_o be an {\it isolated} point of the spectrum of A.
In addition, let \lambda_o be an {\it eigenvalue} of A:
\lambda_o \in \sigma_{pp}(A) .
The question is:
Is \lambda_o an eigenvalue of B ?
And, if so, is the multiplicity of \lambda_o in \sigma_{pp}(B)
equal to the multiplicity of
\lambda_o in \sigma_{pp}(A) ? -- or less? -- or greater?
Keywords: M.G.Krein's Formula, Finite Rank Perturbation.