\(M\)-ideals and the ``basic inequality''
type: Item
instance of: scholarly article
title: \(M\)-ideals and the ``basic inequality''
zbMATH Open document ID: 0797.41019
published in: Journal of Approximation Theory
publication date: 1994-10-09T00:00:00Z
review text: It can be shown that, on a Banach space \(X\), every bounded linear operator has a best compact approximation, both by the basic inequality method and the method of \(M\)-ideals. In the present paper these methods are shown to be basically equivalent. The possibility of such a relationship was raised in \textit{S. Axler}, \textit{I. D. Berg}, \textit{N. Jewell} and \textit{A. Shields} [Ann. Math., II. Ser. 109, 601-612 (1979; Zbl 0399.47024)] and \textit{S. Axler}, \textit{N. Jewell} and \textit{A. Shields} [Trans. Am. Math. Soc. 261, 159-167 (1980; Zbl 0434.41016)].
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 502995
zbMATH Keywords: best compact approximation
zbMATH Keywords: \(M\)-ideals
author: Dirk Werner
reviewed by: H. R. Dowson
MaRDI profile type: Publication
full work available at URL: jath.1994.1002
OpenAlex ID: W2024473998
DOI: 10.1006/JATH.1994.1002
description: scientific article; zbMATH DE number 502995