This is an announcement for the paper "Szlenk and $w^\ast$-dentability indices of the Banach spaces $C([0,\alpha])$" by Philip A.H. Brooker.
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 $\omega^{1+\gamma+1}$.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B20
Submitted from: philip.a.h.brooker@gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.3696
or