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  • 1 Isparta Vocational School, University of Suleyman Demirel, 32260 Isparta, Turkey
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Abstract

We study the spectral multiplicity for the direct sum AB of operators A and B on the Banach spaces X and Y. Under some domination conditions ‖P(B)‖≦CP(A)‖, in particular, ‖Bn‖≦CAn‖, n≧0, we prove the addition formulas μ(AB)=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 TA, where T is a weighted shift operator on the Wiener algebra .

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
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per Year
3
Issues
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6
Founder Magyar Tudományos Akadémia
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Springer Nature Switzerland AG
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ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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