Abstract
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 [12]. 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 \(W(\mathbb{D})\).
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