Proximinality of certain subspaces of \(C_ b(S;E)\)
type: Item
instance of: scholarly article
title: Proximinality of certain subspaces of \(C_ b(S;E)\)
zbMATH Open document ID: 0699.41035
DOI: 10.1216/RMJ-1989-19-1-335
author: Ary O. Chiacchio
author: João B. Prolla
published in: Rocky Mountain Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: Let S be a completely regular Hausdorff space and let E be a Banach space. Let \(C_ b(S;E)\) be the Banach space of all continuous and bounded functions from S into E, equipped with the supremum-norm \(\| f\| =\sup \{\| f(x)\|;\quad x\in S\}.\) Given a proximinal linear subspace V of E, we study conditions under which the space \(\{f\in C_ b(S;E)\); f(S)\(\subset V\}\) is also proximinal in \(C_ b(S;E)\).
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 4146785
zbMATH Keywords: proximinal subspace
zbMATH Keywords: proximity maps
reviewed by: João B. Prolla
MaRDI profile type: Publication
full work available at URL: rmj-1989-19-1-335
OpenAlex ID: W2077726899
description: scientific article; zbMATH DE number 4146785