RT Journal Article
T1 Renorming Banach spaces with the Mazur intersection property
A1 Jiménez Sevilla, María Del Mar
A1 Moreno, José Pedro
AB 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.
PB Elsevier
SN 0022-1236
YR 1997
FD 1997-03
LK https://hdl.handle.net/20.500.14352/58703
UL https://hdl.handle.net/20.500.14352/58703
LA eng
NO 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.
NO DGICYT
DS Docta Complutense
RD 11 may 2025