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A constant of porosity for convex bodies

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Jiménez Sevilla, María del Mar and Moreno, José Pedro (2001) A constant of porosity for convex bodies. Illinois Journal of Mathematics, 45 (3). pp. 1061-1071. ISSN 0019-2082

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Abstract

It was proved recently that a Banach space fails the Mazur intersection property if and only if the family of all closed, convex and bounded subsets which are intersections of balls is uniformly very porous. This paper deals with the geometrical implications of this result. It is shown that every equivalent norm on the space can be associated in a natural way with a constant of porosity, whose interplay with the geometry of the space is then investigated. Among other things, we prove that this constant is closely related to the set of ε-differentiability points of the space and the set of r-denting points of the dual. We also obtain estimates for this constant in several classical spaces.


Item Type:Article
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Supported in part by DGICYT Grant BMF-2000-0609.The authors wish to thank the C.E.C.M., the Department of Mathematics and Statistics at Simon Fraser University, and especially J. Borwein, for their hospitality during the preparation of this paper.

Uncontrolled Keywords:Uniformly very porous; Set of weak denting points; Differentiability points; Constant of porosity; Mazur intersection property; Equivalent norm
Subjects:Sciences > Mathematics > Differential geometry
ID Code:16429
Deposited On:19 Sep 2012 08:14
Last Modified:27 Jul 2018 07:44

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