%0 Journal Article
%A Jiménez Sevilla, María Del Mar
%A Moreno, José Pedro
%T Renorming Banach spaces with the Mazur intersection property
%D 1997
%@ 0022-1236
%U https://hdl.handle.net/20.500.14352/58703
%X In this paper we give new sufficient and necessary conditions for a Banach space to be equivalently renormed with the Mazur intersection property. As a consequence, several examples and applications of these results are obtained. Among them, it is proved that every Banach space embeds isometrically into a Banach space with the Mazur intersection property, answering a question asked by Giles, Gregory, and Sims. We also prove that for every treeT, the spaceC0(T) admits a norm with the Mazur intersection property, solving a problem posed by Deville, Godefroy, and Zizler. Finally, assuming the continuum hypothesis, we find an example of an Asplund space admitting neither an equivalent norm with the above property nor a nicely smooth norm.
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