A theorem on splitting an operator, and some related questions in the analytic theory of perturbations

The basis for most of the results in this paper is a theorem that a perturbed operator with disjoint parts of the spectrum is similar to an operator for which the subspaces constructed from the isolated parts of the unperturbed operator are invariant. In particular, estimates are obtained for the eigenvalues and projections of the perturbed operators, results about equiconvergence of spectral decompositions are obtained, and convergence questions for the eigenvalues are investigated with the use of projection methods.
Bibliography: 15 titles.