Concerning weak$^*$-extreme points
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 245-248.

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Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak$^*$-extreme points of the unit ball is discrete.
Classification : 46B03, 46B20
Keywords: weak$^*$-extreme points; equivalent norm; nonreflexive Banach spaces
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Matoušková, Eva. Concerning weak$^*$-extreme points. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 245-248. http://geodesic.mathdoc.fr/item/CMUC_1995__36_2_a3/