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Antiproximinal convex bounded sets in the space c0(Γ) equipped with the day norm |
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| Authors: | V S Balaganskii |
| Institution: | (1) Institute of Mathematics and Mechanics, Ural Division, Russian Academy of Sciences, Russia |
| Abstract: | We construct a convex smooth antiproximinal set in any infinite-dimensional space c 0(Γ) equipped with the Day norm; moreover, the distance function to the set is Gâteaux differentiable at each point of the complement. |
| Keywords: | antiproximinal set Banach space Gateaux differentiability Day norm the Hahn— Banach theorem weakly compact set |
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