×

A characterization of weakly sequentially complete Banach lattices. (English) Zbl 0587.46019

In this paper we characterize the measures with values in a weakly sequentially complete Banach lattice which have a Radon-Nikodym derivative. Conversely, if we want to obtain such a characterization for a Banach lattice, the Banach lattice must be weakly sequentially complete.

MSC:

46B42 Banach lattices
46G10 Vector-valued measures and integration
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Aliprantis, C.D., Burkinshaw, O., Duhoux, M.: Compactness properties of abstract kernel operators. Pac. J. Math.100, 1-22 (1982) · Zbl 0452.47037
[2] Caselles, V.: Radon-Nikodym derivatives inAL-spaces (preprint)
[3] Diestel, J., Uhl, J.J. Jr.: Vector measures. AMS Mathematical Surveys15 (1977) · Zbl 0369.46039
[4] Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II: Function spaces. Berlin-Heidelberg-New York: Springer 1979 · Zbl 0403.46022
[5] Meyer-Nieberg, P.: Charakterisierung einiger topologischer und ordnungstheoretischer Eigenschaften von Banachverb?nden mit Hilfe disjunkter Folgen. Arch. Math.24, 640-647 (1973) · Zbl 0275.46005 · doi:10.1007/BF01228263
[6] Schaefer, H.H.: Banach lattices and positive operators. Berlin-Heidelberg-New York: Springer 1974 · Zbl 0296.47023
[7] Schmidt, K.D.: The Jordan decomposition for vector measures (preprint)
[8] Talagrand, M.: Quand l’espace des mesures a variation born?e est-il faiblement sequentiellement complet? Proc. Am. Math. Soc.90, 285-288 (1984) · Zbl 0534.46017
[9] Zaanen, A.C.: Riesz Spaces II. Amsterdam: North Holland 1983 · Zbl 0519.46001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.