The Extreme Points of the Unit Ball of the James space $J$ and its dual spaces

TL;DR

This paper offers new proofs and explicit descriptions of the extreme points of the unit balls in James space and its duals, revealing deep structural insights into their geometric properties.

Contribution

It provides a new proof of Bellenot's characterization and explicit descriptions of extreme points for James space and its duals, enhancing understanding of their geometry.

Findings

Explicit descriptions of extreme points of $B_J$ and $B_{J^{**}}$

Characterization of extreme points of $B_{J^*}$ and its norm closure

Connections between extreme points of $B_J$ and $B_{J^*}$

Abstract

We provide a new proof of S. Bellenot's characterization of the extreme points of the unit ball $B_J$ of James quasi-reflexive space $J$. We also provide an explicit description of the norm of $J^{**}$ which yields an analogous characterization for the extreme points of $B_{J^{**}}$. In the last part of the paper we describe the set of all extreme points of $B_{J^*}$ and its norm closure. It is remarkable that the descriptions of the extreme points of $B_J$ and $B_{J^*}$ are closely connected.