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

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.