Three-space property for asymptotically uniformly smooth renormings
Functional Analysis
2012-09-10 v1
Abstract
We prove that if is a closed subspace of a Banach space such that and admit an equivalent asymptotically uniformly smooth norm, then 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.
Keywords
Cite
@article{arxiv.1209.1567,
title = {Three-space property for asymptotically uniformly smooth renormings},
author = {P. A. H. Brooker and G. Lancien},
journal= {arXiv preprint arXiv:1209.1567},
year = {2012}
}