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Functions of bounded semivariation and countably additive vector measures

  • In the Banach space co there exists a continuous function of bounded semivariation which does not correspond to a countably additive vector measure. This result is in contrast to the scalar case, and it has consequences for the characterization of scalar-type operators. Besides this negative result we introduce the notion of functions of unconditionally bounded variation which are exactly the generators of countably additive vector measures.

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Author:Peter Vieten
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7929
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (297)
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:Function of bounded variation; Integral transform
Source:zusammen mit L. Weis, in: LSU Seminar Notes in Functional Analysis and PDE" s 1992/93, Baton Rouge(1993).
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011