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.
Author: | Peter Vieten |
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URN: | urn:nbn:de:hbz:386-kluedo-7929 |
Series (Serial Number): | Preprints (rote Reihe) des Fachbereich Mathematik (297) |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 1997 |
Year of first Publication: | 1997 |
Publishing Institution: | 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: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |