Unit balls of polyhedral Banach spaces with many extreme points
Volume 275 / 2024
Studia Mathematica 275 (2024), 175-196
MSC: Primary 46B20; Secondary 52B99
DOI: 10.4064/sm230710-31-12
Published online: 20 May 2024
Abstract
Let $E$ be a (IV)-polyhedral Banach space. We show that, for each $\epsilon \gt 0$, $E$ admits an $\epsilon $-equivalent (V)-polyhedral norm such that the corresponding closed unit ball is the closed convex hull of its extreme points. In particular, every separable isomorphically polyhedral Banach space has this property.
