Renorming Banach spaces with the Mazur intersection property

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Jiménez Sevilla, María del Mar and Moreno, José Pedro (1997) Renorming Banach spaces with the Mazur intersection property. Journal of Functional Analysis, 144 (2). pp. 486-504. ISSN 0022-1236

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022123696930141#




Abstract

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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Additional Information:

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.

Subjects:Sciences > Mathematics > Algebra
ID Code:22592
Deposited On:27 Aug 2013 07:07
Last Modified:27 Jul 2018 07:56

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