The Mazur intersection property and Asplund spaces

Abstract

We answer a question posed by J. R. Giles, D. A.
Gregory and B. Sims, on the Mazur intersection property, by exhibiting a class of non Asplund spaces admitting an equivalent norm with the above property. On the other hand, if the continuum hypothesis is assumed, we nd an Asplund space admitting no equivalent norm with the Mazur intersection property and whose dual space admits no equivalent norm with the weak* Mazur intersection property.