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A note on the relationship between the Szlenk and $w^*$-dentability indices of arbitrary $w^*$-compact sets (1608.03668v1)

Published 12 Aug 2016 in math.FA

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.

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