RENORMING BANACH-SPACES WITH THE MAZUR INTERSECTION PROPERTY

In this paper we give new sufficient and necessary conditions:for a Ba nach space to be equivalently renormed with the Mazur intersection pro perty, As a consequence, several examples and applications of these re sults are obtained. Among them. it is proved that every Banach space e mbeds isometrically into a Banach space with the Mazur intersection pr operty, answering a question asked by Giles, Gregory, and Sims. We als o prove that for every tree T, the space C-0(T) admits a norm with the Mazur intersection property, solving a problem posed by Deville, Gode froy, and Zizler. Finally, assuming the continuum hypothesis, we find an example of an Asplund space admitting neither an equivalent norm wi th the above property nor a nicely smooth norm. (C) 1997 Academic Pres s.