English

Three-space property for asymptotically uniformly smooth renormings

Functional Analysis 2012-09-10 v1

Abstract

We prove that if YY is a closed subspace of a Banach space XX such that YY and X/YX/Y admit an equivalent asymptotically uniformly smooth norm, then XX 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}
}
R2 v1 2026-06-21T22:01:36.214Z