Antiproximinal Norms in Banach Spaces
نویسندگان
چکیده
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.
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ورودعنوان ژورنال:
- Journal of Approximation Theory
دوره 114 شماره
صفحات -
تاریخ انتشار 2002