This is an announcement for the paper "Three-space property for asymptotically uniformly smooth renormings" by P.A.H. Brooker and G. Lancien.

Abstract: We prove that if $Y$ is a closed subspace of a Banach space $X$ such that $Y$ and $X/Y$ admit an equivalent asymptotically uniformly smooth norm, then $X$ also admits an equivalent asymptotically uniformly smooth norm. The proof is based on the use of the Szlenk index and yields a few other applications to renorming theory.

Archive classification: math.FA

Submitted from: gilles.lancien@univ-fcomte.fr

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

http://front.math.ucdavis.edu/1209.1567

or

http://arXiv.org/abs/1209.1567