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Characterization of operators of positive scalar type

  • Let \(X\) be a Banach lattice. Necessary and sufficient conditions for a linear operator \(A:D(A) \to X\), \(D(A)\subseteq X\), to be of positive \(C^0\)-scalar type are given. In addition, the question is discussed which conditions on the Banach lattice imply that every operator of positive \(C^0\)-scalar type is necessarily of positive scalar type.

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Author:Peter Vieten
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7560
Document Type:Article
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Banach lattice; Scalar type operator
Source:Proceedings of the Prague Mathematical Conference 1996, Prague (1996), 331-336.
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