Jiménez Sevilla, María Del MarMoreno, José Pedro2023-06-202023-06-201997-030022-123610.1006/jfan.1996.3014https://hdl.handle.net/20.500.14352/58703We thank G. Godefroy for Corollaries 2.8 and 4.4 as well as for many other helpful suggestions. We also thank J. Gomez and S. L. Troyanski for valuable discussions and comments.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.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022123696930141#http://www.sciencedirect.com/restricted access512Álgebra1201 Álgebra