Spectral analysis of perturbed nonquasianalytic and spectral operators

Theorems on similarity of perturbed nonquasianalitic (in the sense of Yu. I. Lyubich and V. I. Matsaev) and spectral (in the sense of Dunford) linear operators with countable partition of their spectra to operators of block-diagonal form are obtained. On the basis of such theorems estimates of spectra and projections are obtained, and the convergence of spectral decompositions of perturbed operators is studied. The results presented in the paper on the (generalized) spectral property of operators substantially strengthen the corresponding results of J. T. Schwartz and H. P. Kramer (see Dunford and Schwartz, Linear operators, vol. III, Chapter XIX).