Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak$^*$-extreme points of the unit ball is discrete.
@article{118752, author = {Eva Matou\v skov\'a}, title = {Concerning weak$^*$-extreme points}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {36}, year = {1995}, pages = {245-248}, zbl = {0831.46010}, mrnumber = {1357525}, language = {en}, url = {http://dml.mathdoc.fr/item/118752} }
Matoušková, Eva. Concerning weak$^*$-extreme points. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 245-248. http://gdmltest.u-ga.fr/item/118752/
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