This article is cited in 1 paper

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

V. S. Balaganskii

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: 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.

UDC: 517.5

Received: 28.04.2004
Revised: 17.06.2005

DOI: 10.4213/mzm2703

 English version: Mathematical Notes, 2006, 79:3, 299–313

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