Strong uniqueness of best approximations in an abstract \(L_ 1\) space
type: Item
instance of: scholarly article
title: Strong uniqueness of best approximations in an abstract \(L_ 1\) space
zbMATH Open document ID: 0675.41048
DOI: 10.1016/0022-247X(88)90089-3
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: If X is a Banach space \(L_ 1(S,\Sigma,\mu)\) when (S,\(\Sigma\),\(\mu)\) is a positive measure space or, equivalently, if X is an abstract \(L_ 1\) space, and M is a finite dimensional subspace of X then the set of elements of X which have a strongly unique best approximation in M is dense in the set of elements which have a unique best approximation in M.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 4105542
zbMATH Keywords: Banach space
zbMATH Keywords: strongly unique best approximation
author: Ryszard Smarzewski
reviewed by: Aldric L. Brown
MaRDI profile type: Publication
cites work: Q3324418
cites work: Q5543516
cites work: Q3935679
cites work: Uniqueness and strong uniqueness of best approximations by spline subspaces and other subspaces
cites work: Strong Unicity of Best Approximations in L ∞ (S, Σ, μ)
cites work: Uniqueness and Differential Characterization of Approximations from Manifolds of Functions
description: scientific article; zbMATH DE number 4105542