English

A note on the relationship between the Szlenk and $w^*$-dentability indices of arbitrary $w^*$-compact sets

Functional Analysis 2016-08-15 v1

Abstract

We prove the optimal estimate between the Szlenk and ww^*-dentability indices of an arbitrary ww^*-compact subset of the dual of a Banach space. For a given ww^*-compact, convex subset KK of the dual of a Banach space, we introduce a two player game the winning strategies of which determine the Szlenk index of KK. We give applications to the ww^*-dentability index of a Banach space and of an operator.

Keywords

Cite

@article{arxiv.1608.03668,
  title  = {A note on the relationship between the Szlenk and $w^*$-dentability indices of arbitrary $w^*$-compact sets},
  author = {Ryan M Causey},
  journal= {arXiv preprint arXiv:1608.03668},
  year   = {2016}
}