Article
Keywords:
weak$^*$-extreme points; equivalent norm; nonreflexive Banach spaces
Summary:
Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak$^*$-extreme points of the unit ball is discrete.
References:
                        
[GLT] Godun B.V., Bor-Luh Lin, Troyanski S.L.: 
On the strongly extreme points of convex bodies in separable Banach spaces. Proc. AMS 114 (1992), 673-675. 
MR 1070518[LP] Lindenstrauss J., Phelps R.R.: 
Extreme point properties of convex bodies in reflexive Banach spaces. Israel J. Math. 6 (1968), 39-48. 
MR 0234260 | 
Zbl 0157.43802[P] Phelps R.R.: 
Dentability and extreme points in Banach spaces. Journal of Functional Analysis 17 (1974), 78-90. 
MR 0352941 | 
Zbl 0287.46026[R] Rosenthal H.P.: 
On norm-attaining functionals and the equivalence of the weak$^*$-KMP with the RNP. Longhorn Notes, The University of Texas at Austin, 1985/86, pp. 1-12. 
MR 1017038[S] Stegall C.: Vorlesungen aus dem Fachbereich Mathematik der Universität Essen. Heft 10, 1983, pp. 1-61.