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Mathematical Notes

, Volume 79, Issue 3–4, pp 299–313 | Cite as

Antiproximinal convex bounded sets in the space c0(Γ) equipped with the day norm

  • V. S. Balaganskii
Article
  • 36 Downloads

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.

Key words

antiproximinal set Banach space Gâteaux differentiability Day norm the Hahn—Banach theorem weakly compact set 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. S. Balaganskii
    • 1
  1. 1.Institute of Mathematics and Mechanics, Ural DivisionRussian Academy of SciencesRussia

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