Antiproximinal convex bounded sets in the space $c_0(\Gamma)$ equipped with the day norm

V. S. Balaganskii

Matematičeskie zametki, Tome 79 (2006) no. 3, pp. 323-338.

Résumé

We construct a convex smooth antiproximinal set in any infinite-dimensional space $c_0(\Gamma)$ equipped with the Day norm; moreover, the distance function to the set is Gâteaux differentiable at each point of the complement.

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