Metric projections in spaces of integrable functions
type: Item
instance of: scholarly article
title: Metric projections in spaces of integrable functions
zbMATH Open document ID: 0827.41020
published in: Journal of Approximation Theory
publication date: 1995-05-18T00:00:00Z
review text: Interest in properties of set valued metric projections arose from attempts to find single valued continuous selections. This work concentrates on the properties of metric projections onto finite dimensional subspaces of spaces of integrable functions. A mapping called ``the derived metric projection'' is constructed. Special cases of the theory developed here are used to recover the best known results. For example, the lower semicontinuous metric projections are completely characterized in this setting. Examples are presented showing that the situations for real and for complex valued functions are fundamentally different. This paper, as well as continuing the list of fundamental contributions by Professor Brown, is also closely related to the 1991 work of \textit{W. Li} [Trans. Am. Math. Soc. 322, No. 2, 583-591 (1990; Zbl 0728.41020)].
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 756643
author: Aldric L. Brown
reviewed by: Daniel Wulbert
MaRDI profile type: Publication
full work available at URL: jath.1995.1034
OpenAlex ID: W2058212082
DOI: 10.1006/JATH.1995.1034
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description: scientific article; zbMATH DE number 756643