Antiproximinal norms in Banach spaces

Title: Antiproximinal norms in Banach spaces
Creator: Borwein, J. M.; Jiménez-Sevilla, M.; Moreno, J. P.
Relation: Journal of Approximation Theory Vol. 114, Issue 1, p. 57-69
Publisher Link: http://dx.doi.org/10.1006/jath.2001.3636
Publisher: Elsevier
Resource Type: journal article
Date: 2002
Description: We prove that every Banach space containing a complemented copy of c₀ has an antiproximinal body for a suitable norm. If, in addition, the space is separable, there is a pair of antiproximinal norms. In particular, in a separable polyhedral space X, the set of all (equivalent) norms on X having an isomorphic antiproximinal norm is dense. In contrast, it is shown that there are no antiproximinal norms in Banach spaces with the convex point of continuity property (CPCP). Other questions related to the existence of antiproximinal bodies are also discussed.
Subject: Banach spaces; antiproximinal norms; approximation; convex sets
Identifier: http://hdl.handle.net/1959.13/940687
Identifier: uon:13078
Identifier: ISSN:0021-9045
Language: eng
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