Polyhedrality and decomposition
Functional Analysis
2022-06-14 v1
Abstract
The aim of this note is to present two results that make the task of finding equivalent polyhedral norms on certain Banach spaces, having either a Schauder basis or an uncountable unconditional basis, easier and more transparent. The hypotheses of both results are based on decomposing the unit sphere of a Banach space into countably many pieces, such that each one satisfies certain properties. Some examples of spaces having equivalent polyhedral norms are given.
Cite
@article{arxiv.1804.06348,
title = {Polyhedrality and decomposition},
author = {Trond A. Abrahamsen and Vladimir P. Fonf and Richard J. Smith and Stanimir Troyanski},
journal= {arXiv preprint arXiv:1804.06348},
year = {2022}
}