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Four characterizations of scalar-type operators with spectrum in a half-line

  • \(C^0\)-scalar-type spectrality criterions for operators \(A\), whose resolvent set contains the negative reals, are provided. The criterions are given in terms of growth conditions on the resolvent of \(A\) and the semi-group generated by \(A\).These criterions characterize scalar-type operators on the Banach space \(X\), if and only if \(X\) has no subspace isomorphic to the space of complex null-sequences.

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Author:Peter Vieten
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7499
Document Type:Preprint
Language of publication:English
Year of Completion:1997
Year of Publication:1997
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Laplace transform; Moment sequence; Scalar-type operator; Stieltjes transform
Source:Studia Math. 122 (1) (1997),39-54.
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):47-XX OPERATOR THEORY / 47Axx General theory of linear operators / 47A60 Functional calculus
47-XX OPERATOR THEORY / 47Bxx Special classes of linear operators / 47B40 Spectral operators, decomposable operators, well-bounded operators, etc.
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011