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Mazur intersection properties for compact and weakly compact convex sets

Published:1998-06-01
Printed: Jun 1998
• Jon Vanderwerff
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Abstract

Various authors have studied when a Banach space can be renormed so that every weakly compact convex, or less restrictively every compact convex set is an intersection of balls. We first observe that each Banach space can be renormed so that every weakly compact convex set is an intersection of balls, and then we introduce and study properties that are slightly stronger than the preceding two properties respectively.
 MSC Classifications: 46B03 - Isomorphic theory (including renorming) of Banach spaces 46B20 - Geometry and structure of normed linear spaces 46A55 - Convex sets in topological linear spaces; Choquet theory [See also 52A07]