Szlenk and $w^\ast$-dentability indices of the Banach spaces $C([0,α])$

Published 13 Oct 2012 in math.FA | (1210.3696v1)

Abstract: Let $\alpha$ be an infinite ordinal and $\gamma$ the unique ordinal satisfying $\omega^{{\omega^\gamma}\leq} \alpha < \omega^{{\omega^{{\gamma+1}}$.}} We show that the Banach space $C([0,\,\alpha])$ of all continuous scalar-valued functions on the compact ordinal interval $[0,\,\alpha]$ has Szlenk index equal to $\omega^{\gamma+1}$ and $w^{\ast$-dentability} index equal to $\omega^{{1+\gamma+1}$.}