On transitivity of proximinality
type: Item
instance of: scholarly article
title: On transitivity of proximinality
zbMATH Open document ID: 0621.41024
DOI: 10.1016/0021-9045(87)90083-9
author: V. Indumathi
published in: Journal of Approximation Theory
publication date: 1987-01-01T00:00:00Z
review text: A normed linear space E is said to be a P(n) space (n\(\geq 2)\) if \(G^{(P)}\subset M\), \(M^{(P)}\subset E\), \(\dim E/G\leq n\Rightarrow G^{(P)}\subset E,\) where G and M are closed subspaces of E and \(G^{(P)}\subset M\) means that G is a proximinal subspace of M. A normed linear space is called a P space if it is a P(n) space for every \(n\geq 2\), i.e. proximinality is transitive. The characterization of P(n) spaces is given. It is proved that \(C_ 0\) and the incomplete inner product spaces are P spaces. It is also proved that the infinite dimensional C(Q) and \(L^ 1(T,v)\) spaces are not P(2) spaces.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46C99
zbMATH DE Number: 4006909
zbMATH Keywords: proximinal subspace
zbMATH Keywords: inner product spaces
MaRDI profile type: Publication
full work available at URL: 0021-9045(87)90083-9
OpenAlex ID: W1999757696
cites work: On the existence of extremal projections
cites work: Q3213662
cites work: Representers of linear functionals, norm-attaining functionals, and best approximation by cones and linear varieties in inner product spaces
cites work: Q3254057
cites work: Q5735446
cites work: THE HELLY PROBLEM AND BEST APPROXIMATION OF SUMMABLE FUNCTIONS
cites work: Q5550654
cites work: Proximinal Subspaces of Finite Codimesion in General Normed Linear Spaces
cites work: Cebysev subspaces of finite codimension in \(C(X)\)
cites work: Q5637350
cites work: Q3286567
cites work: A smooth, non-reflexive second conjugate space
cites work: Q3050961
description: scientific article; zbMATH DE number 4006909