Asymptotic intertwining and spectral inclusions on Banach spaces
Kjeld Bagger Laursen, Michael M. Neumann (1993)
Czechoslovak Mathematical Journal
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Kjeld Bagger Laursen, Michael M. Neumann (1993)
Czechoslovak Mathematical Journal
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Elbjaoui, H., Zerouali, E. H. (2003)
International Journal of Mathematics and Mathematical Sciences
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Mihai Putinar (1997)
Banach Center Publications
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The paper relates several generalized eigenfunction expansions to classical spectral decomposition properties. From this perspective one explains some recent results concerning the classes of decomposable and generalized scalar operators. In particular a universal dilation theory and two different functional models for related classes of operators are presented.
Vladimír Müller (1988)
Czechoslovak Mathematical Journal
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B. Aupetit, D. Drissi (1994)
Studia Mathematica
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In 1971, Allan Sinclair proved that for a hermitian element h of a Banach algebra and λ complex we have ∥λ + h∥ = r(λ + h), where r denotes the spectral radius. Using Levin's subordination theory for entire functions of exponential type, we extend this result locally to a much larger class of generalized spectral operators. This fundamental result improves many earlier results due to Gelfand, Hille, Colojoară-Foiaş, Vidav, Dowson, Dowson-Gillespie-Spain, Crabb-Spain, I. & V. Istrăţescu,...