  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
