Best approximation in polyhedral Banach spaces
type: Item
instance of: scholarly article
title: Best approximation in polyhedral Banach spaces
zbMATH Open document ID: 1229.41027
author: V. P. Fonf
author: J. Lindenstrauss
author: Libor Vesely
published in: Journal of Approximation Theory
publication date: 2011-10-28T00:00:00Z
review text: The authors study conditions under which the metric projection of a polyhedral Banach space \(X\) onto a closed subspace \(Y\) is Hausdorff lower or upper semicontinuous. The paper is organized as follows. Section 0 is an introduction. Section 1 contains notation concerning Banach spaces, followed by definitions and preliminary facts on polyhedral Banach spaces. Section 2 is a collection of preliminaries concerning metric projections onto closed subspaces. Sections 3 and 4 deal with (semi)continuity properties of the metric projection \(P_Y\) under polyhedrality-type assumptions on \(X\). Section 5 contains results on the proximinality of subspaces and polyhedrality of quotients. Sections 6, 7 and 8 contain one example each. These examples illustrate the importance of some of the hypotheses in the main results.
reviewed by: Richard A. Zalik
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 5965565
zbMATH Keywords: polyhedral Banach space
zbMATH Keywords: metric projection
zbMATH Keywords: proximininal subspace
MaRDI profile type: Publication
full work available at URL: j.jat.2011.06.011
OpenAlex ID: W2076209880
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DOI: 10.1016/J.JAT.2011.06.011
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description: scientific article; zbMATH DE number 5965565