The closure in a Hilbert space of a preHilbert space Chebyshev set that fails to be a Chebyshev set

JOURNAL OF APPROXIMATION THEORY

卷:203

Article

Johnson, Gordon G.¹ 

[1] Univ Houston, Dept Math, Houston, TX 77204 USA

关键词: Convex;    Unique nearest point;    Euclidean space;    Hilbert space approximation;    Chebyshev set;   

DOI  :  10.1016/j.jat.2015.11.004

来源: Elsevier

【 摘 要 】

In 1987 the author gave an example of a non convex Chebyshev set S in the incomplete inner product space E consisting of the vectors in l(2) which have at most a finite number of non zero terms. In this paper, we show that the closure of S in the Hilbert space completion l(2) of E is not Chebyshev in l(2). (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free