On the structure of non dentable subsets of C({\omega}^{\omega}^k)
Functional Analysis
2011-03-03 v1
Abstract
It is shown that there is no K closed convex bounded non-dentable subset of C({\omega}^{\omega} ^k) such that on the subsets of K the PCP and the RNP are equivalent properties. Then applying Schachermayer-Rosenthal theorem, we conclude that every non-dentable K contains non-dentable subset L so that on L the weak topology coincides with the norm one. It follows from known results that the RNP and the KMP are equivalent properties on the subsets of C({\omega}^{\omega} ^k).
Keywords
Cite
@article{arxiv.1103.0366,
title = {On the structure of non dentable subsets of C({\omega}^{\omega}^k)},
author = {Pericles D Pavlakos and Minos Petrakis},
journal= {arXiv preprint arXiv:1103.0366},
year = {2011}
}
Comments
18 pages,accepted in Studia Mathematica