Cominimal projections in \(l_\infty^n\)
type: Item
instance of: scholarly article
title: Cominimal projections in \(l_\infty^n\)
zbMATH Open document ID: 0936.41018
author: Agnieszka Lipieta
published in: Journal of Approximation Theory
publication date: 1999-04-27T00:00:00Z
review text: The paper investigates the constant \(\lambda_I(Y,l^n_\infty)\), the infimum of \(\|I-P\|\) over all linear projections \(P\) of \(l^n_\infty\) onto \(Y\), where \(Y\) is a subspace of \(l^n_\infty\) of codimension two; a projection \(P\) is cominimal if \(\|I-P\|=\lambda_I (Y,l^n_\infty)\). Those \(Y\) such that \(\lambda_I(Y,l^n_\infty)=1\) are completely characterised. For \(Y\) such that \(\lambda_I(Y,l^n_\infty)>1\) an estimate from below is obtained. Illustrative examples in the cases \(n=3,4,5,7\) are calculated.
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 1251373
reviewed by: Aldric L. Brown
MaRDI profile type: Publication
full work available at URL: jath.1998.3221
OpenAlex ID: W2071879410
cites work: Minimal projections on hyperplanes in sequence spaces
cites work: Q5543516
cites work: Approximation theory in tensor product spaces
cites work: The Determination of Minimal Projections and Extensions in L 1
cites work: Q4838510
cites work: Q5620940
cites work: Unique Minimality of Fourier Projections
cites work: Projections onto hyperplanes in Banach spaces
cites work: Norms of minimal projections
cites work: Minimal projections onto two dimensional subspaces of \(l_ \infty^{(4)}\)
cites work: Minimal projections in Banach spaces. Problems of existence and uniqueness and their application
cites work: Extreme points in duals of operator spaces
cites work: Q3483775
DOI: 10.1006/JATH.1998.3221
description: scientific article; zbMATH DE number 1251373