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

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 $J^{\ast \ast }$ which yields an analogous characterization for the extreme points of $B_{J^{\ast \ast }}$. In the last part of the paper we describe the set of all extreme points of $B_{J^{\ast }}$ and its norm closure. It is remarkable that the descriptions of the extreme points of $B_J$ and $B_{J^{\ast }}$ are closely connected.

28 pages