2026-08-22T00:38:52Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/587032025-01-20T16:50:28Zcom_20.500.14352_14col_20.500.14352_15

Renorming Banach spaces with the Mazur intersection property Jiménez Sevilla, María Del Mar Moreno, José Pedro 512 Álgebra 1201 Álgebra We 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. DGICYT Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T18:49:23Z 2023-06-20T18:49:23Z 1997-03 journal article https://hdl.handle.net/20.500.14352/58703 0022-1236 10.1006/jfan.1996.3014 eng PB 93-0452 restricted access application/pdf Elsevier