Preprints (rote Reihe) des Fachbereich Mathematik
- 297
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Functions of bounded semivariation and countably additive vector measures
(1997)
- 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.
