Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T13:13:21.816Z Has data issue: false hasContentIssue false
  • English
  • Français

On Dunford-Pettis Operators

Published online by Cambridge University Press:  20 November 2018

Elias Saab
Elias Saab*
Affiliation:
The University of British Columbia, Vancouver, B.C. V6T1Y4, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let X be a complemented subspace of a Banach lattice E. It is shown that if every Dunford-Pettis operator from L1[0,1] into X is Pettis-representable then X has the Radon-Nikodym property.

Keywords

46G1046B22Dunford-Pettis operatorsRadon-Nikodym property
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 2 , 01 June 1982 , pp. 207 - 209
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Bourgain, J., Dunford-Pettis Operators and the Radon-Nikodym property, (preprint).Google Scholar
2. Diestel, J. and Uhl, J. J. Jr., Vector measures, Mathematical Survey No. 15, American Mathematical Society, Providence, 1977.Google Scholar
3. Fremlin, D. H., Pointwise compact subsets of measurable functions, Manuscripts Math. 15, 219-242 (1975).Google Scholar
4. Ghoussoub, N. and Saab, E., On the weak Radon-Nikodym property, Proc. Amer. Math. Soc. 81 (1981), 81-84.Google Scholar
5. Janicka, L., Wlasnosci Typu Radona-Nikodyma dla Przestrzeni Banacha, Thesis, 1978, Wroclaw.Google Scholar
6. Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces II, Springer-Verlag (1979).Google Scholar
7. Sierpinski, W., Fonctions additives non completement additives et fonctions non mesurables. Fund. Math. 30 (96-99) 1938.Google Scholar