[Banach] Abstract of a paper by Petr Hajek and Thomas Schlumprecht

This is an announcement for the paper "The Szlenk index of L_p(X)" by Petr Hajek and Thomas Schlumprecht.

Abstract: We find an optimal upper bound on the values of the weak$^*$-dentability index $Dz(X)$ in terms of the Szlenk index $Sz(X)$ of a Banach space $X$ with separable dual. Namely, if $;Sz(X)=\omega^{\alpha}$, for some $\alpha<\omega_1$, and $p\in(1,\infty)$, then $$Sz(X)\le Dz(X)\le Sz(L_p(X))\le \begin{cases} \omega^{\alpha+1} &\text{ if $\alpha$ is a finite ordinal,} \omega^{\alpha} &\text{ if $\alpha$ is an infinite ordinal.} \end{cases}$$

Archive classification: math.FA

Mathematics Subject Classification: 46B03 46B10

Submitted from: schlump@math.tamu.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1308.3629

or

http://arXiv.org/abs/1308.3629