Nondentable Sets in Banach Spaces
Functional Analysis
2020-03-02 v2
Abstract
In his study of the Radon Nikod\'ym property of Banach spaces, Bourgain showed (among other things) that in any closed, bounded, convex set that is nondentable, one can find a separated, weakly closed bush. In this note, we prove a generalization of Bourgain's result: in any bounded, nondentable set (not necessarily closed or convex) one can find a separated, weakly closed approximate bush. Similarly, we obtain as corollaries the existence of -valued quasimartingales with sharply divergent behavior.
Cite
@article{arxiv.1910.11962,
title = {Nondentable Sets in Banach Spaces},
author = {S. J. Dilworth and Chris Gartland and Denka Kutzarova and N. Lovasoa Randrianarivony},
journal= {arXiv preprint arXiv:1910.11962},
year = {2020}
}
Comments
9 pages