Jos Pedro Moreno, Rolf Schneider
Intersection properties of polyhedral norms
We investigate the family of intersections of balls in a finite-dimensional vector space with a polyhedral norm. The spaces for which is closed under Minkowski addition are completely determined. We characterize also the polyhedral norms for which is closed under adding a ball. A subset of consists of the Mazur sets K, defined by the property that for any hyperplane H not meeting K there is a ball containing K and not meeting H. We characterize the Mazur sets in terms of their normal cones and also as summands of closed balls. As a consequence, we characterize the polyhedral spaces with only trivial Mazur sets as those whose unit ball is indecomposable.
Advances in Geometry, Walter de Gruyter
Print ISSN: 1615-715X
Volume: 7, 07/2007
Pages: 391 - 402
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