Minimal projections onto two dimensional subspaces of \(l_ \infty^{(4)}\)
type: Item
instance of: scholarly article
title: Minimal projections onto two dimensional subspaces of \(l_ \infty^{(4)}\)
zbMATH Open document ID: 0866.41020
author: Grzegorz Lewicki
published in: Journal of Approximation Theory
publication date: 1997-04-08T00:00:00Z
review text: Let \((X,|\cdot|)\) be a normed linear space. Let \(Y\subseteq X\), and let \(F\) be some collection of operators from \(X\) into \(Y\). The general problem related to this paper is that of identifying the operators in \(F\) of minimal norm. For example, classically important results include the cases when \(X= C[-1,1]\) or \(C_{2\pi}\), \(Y\) is respectively the polynomials of degree \(n\) or the trigonometric polynomials of degree \(n\), and \(F\) is respectively the interpolating projections or the set of all projections. This paper identifies the minimal projections from the 4-dimensional space with the maximum norm onto 2-dimensional subspaces. The statement of the theorem is very long and technical. The paper also determines when the minimal projection is unique.
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 41A45
zbMATH DE Number: 980682
reviewed by: Daniel Wulbert
MaRDI profile type: Publication
full work available at URL: jath.1996.3014
OpenAlex ID: W2035808030
DOI: 10.1006/JATH.1996.3014
description: scientific article; zbMATH DE number 980682