Hostname: page-component-669899f699-7tmb6 Total loading time: 0 Render date: 2025-04-27T17:01:39.096Z Has data issue: false hasContentIssue false
  • English
  • Français

Slices, RNP, strong regularity, and martingales

Published online by Cambridge University Press:  17 April 2009

Maria Girardi  and
J.J. Uhl Jr
Maria Girardi
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green St, Urbana, IL 61801, United States of America
J.J. Uhl Jr
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green St, Urbana, IL 61801, United States of America
Rights & Permissions [Opens in a new window]

Extract

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.

The usual proof that dentability implies the Radon-Nikodým property involves a clever but rather baroque exhaustion argument. This note presents a very short and simple proof of this implication. The techniques in this new proof are then generalised to derive some direct proofs of recent results concerning strongly regular operators on L1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 3 , June 1990 , pp. 411 - 415
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Bourgain, J., ‘Dunford-Pettis operators on L 1 and the Radon-Nikodým property’, Israel J. Math. 37 (1980), 34–47.CrossRefGoogle Scholar
[2]Diestel, J. and Uhl, J. J. Jr., Vector Measures, Math. Surveys, no. 15 (American Mathethematical Society, Providence, R.I., 1977).CrossRefGoogle Scholar
[3]Ghoussoub, N., Godefroy, G., Maurey, B., and Schachermayer, W., ‘Some topological and geometrical structures in Banach spaces’, in Mem. American Mathematical Society, 70, no. 378 (Amer. Math. Soc., Providence, R.I., 1987).Google Scholar