RT Journal Article
T1 A constant of porosity for convex bodies
A1 Jiménez Sevilla, María Del Mar
A1 Moreno, José Pedro
AB 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.
PB University of Illinois
SN 0019-2082
YR 2001
FD 2001
LK https://hdl.handle.net/20.500.14352/57536
UL https://hdl.handle.net/20.500.14352/57536
LA eng
NO 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.
NO DGICYT
DS Docta Complutense
RD 8 abr 2025