We study the spectral multiplicity for the direct sum A⊕B of operators A and B on the Banach spaces X and Y. Under some domination conditions ‖P(B)‖≦C‖P(A)‖, in particular, ‖Bn‖≦C‖An‖, n≧0, we prove the addition formulas μ(A⊕B)=μ(A)+μ(B) for spectral multiplicities. We give valuable new applications of the main result of the author’s paper . We also use the so-called Borel transformation and generalized Duhamel product in calculating the spectral multiplicity of a direct sum of the form T⊕A, where T is a weighted shift operator on the Wiener algebra .
 Colojoara, I. and Foias, C., The Theory of Generalized Spectral Operators, Cordon and Breach (N.Y., 1968).
Colojoara, I. and Foias, C., The Theory of Generalized Spectral Operators, Cordon and Breach (N.Y., 1968).)| false
Karaev, M. T.2005On some applications of the ordinary and extended Duhamel productsSiberian Math. J.46431–44210.1007/s11202-005-0046-6. translated from Sibirskii Matem. Zhurnal, 46 (2005), 553–566.)| false