[Banach] Abstract of a paper by Ryan M Causey

This is an announcement for the paper “A note on the relationship between the Szlenk and w∗-dentability indices of arbitrary w∗-compact sets” by Ryan M Causeyhttp://arxiv.org/find/math/1/au:+Causey_R/0/1/0/all/0/1.

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

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1608.03668