[Banach] Abstract of a paper by Pericles D Pavlakos and Minos Petrakis

This is an announcement for the paper "On the structure of non dentable subsets of C({\omega}^{\omega}^k)" by Pericles D Pavlakos and Minos Petrakis.

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).

Archive classification: math.FA

Remarks: 18 pages,accepted in Studia Mathematica

Submitted from: minos@science.tuc.gr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1103.0366

or

http://arXiv.org/abs/1103.0366