- 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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