Home >> Mathematical Notes, Volume 79, Number 3

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

Author: Balaganskii, V.

Source: Mathematical Notes, Volume 79, Number 3, March 2006 , pp. 299-313(15)

Publisher: Springer

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

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s11006-006-0035-5

Affiliations: 1: Email: Vladimir.Balaganskii@imm.uran.ru

Publication date: 2006-03-01

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