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Antiproximinal sets in the Banach space \(c( X)\). (English) Zbl 0887.41029
The author proves the existence of antiproximinal convex cell in the Banach space \(c(X)\) of all \(X\)-valued convergence sequences, where \(X\) is a non-trivial Banach space (i.e. the existence a nonvoid bounded closed convex body \(V\) such that no point in \(c(X)\setminus V\) has a nearest point in \(V\)). The case of the space \(c_0(X)\) was considered in the author’s earlier paper [Mat. Zametki 17, 449-457 (1975; Zbl 0327.41030)].
Reviewer: K.Najzar (Praha)

MSC:
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A50 Best approximation, Chebyshev systems
46B99 Normed linear spaces and Banach spaces; Banach lattices
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