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T. L. Miller, Michael M. Neumann (2002)
Czechoslovak Mathematical Journal
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It is shown that the sum and the product of two commuting Banach space operators with Dunford’s property have the single-valued extension property.
Che-Kao Fong (1979)
Studia Mathematica
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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.
Ştefan Frunzǎ (1982)
Banach Center Publications
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Elbjaoui, H., Zerouali, E. H. (2003)
International Journal of Mathematics and Mathematical Sciences
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P. A. Cojuhari, A. M. Gomilko (2008)
Studia Mathematica
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The paper is concerned with conditions guaranteeing that a bounded operator in a reflexive Banach space is a scalar type spectral operator. The cases where the spectrum of the operator lies on the real axis and on the unit circle are studied separately.
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,...