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

We provide a new proof of S. Bellenot's characterization of the extreme points of the unit ball BJ 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 BJ^* and its norm closure. It is remarkable that the descriptions of the extreme points of BJ and BJ^* are closely connected.