A topological characterization of dual strict convexity in Asplund spaces

Richard J. Smith

doi:10.1016/j.jmaa.2019.123806

A topological characterization of dual strict convexity in Asplund spaces

Functional Analysis 2022-06-14 v1

Authors: Richard J. Smith

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

Let $X$ be an Asplund space. We show that the existence of an equivalent norm on $X$ having a strictly convex dual norm is equivalent to the dual unit sphere $S_{X^*}$ (equivalently $X^*$ ) possessing a non-linear topological property called ( $*$ ), which was introduced by J. Orihuela, S. Troyanski and the author.

Keywords

asplund space strictly convex dual norm equivalent norm dual unit sphere topological property

Cite

@article{arxiv.1909.00678,
  title  = {A topological characterization of dual strict convexity in Asplund spaces},
  author = {Richard J. Smith},
  journal= {arXiv preprint arXiv:1909.00678},
  year   = {2022}
}

Related papers

View all related →