Notes on Rank One Perturbed Resolvent. Perturbation of Isolated Eigenvalue
Mathematical Physics
2016-09-07 v2 Dynamical Systems
math.MP
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
Keywords
Cite
@article{arxiv.math-ph/0312070,
title = {Notes on Rank One Perturbed Resolvent. Perturbation of Isolated Eigenvalue},
author = {Sergej A. Choroszavin},
journal= {arXiv preprint arXiv:math-ph/0312070},
year = {2016}
}
Comments
Latex 2.09