Antiproximinal norms in Banach spaces

Borwein, Jonathan M. and Jimenez-sevilla, M. and Moreno, J.P (2002) Antiproximinal norms in Banach spaces. J. Approx. Theory, 114 . pp. 57-69.

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      We prove that every Banach space containing a complemented copy of $c_0$ has an antipro\-ximinal 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.

      Item Type: Article
      Additional Information: pubdom FALSE
      Subjects: 46-xx Functional analysis > 46Bxx Normed linear spaces and Banach spaces; Banach lattices
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 28 Nov 2003
      Last Modified: 28 Sep 2014 14:43

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