Norm attaining multilinear forms on \(L_{1}(\mu )\)
type: Item
instance of: scholarly article
title: Norm attaining multilinear forms on \(L_{1}(\mu )\)
zbMATH Open document ID: 1156.46015
DOI: 10.1155/2008/328481
author: Yousef Saleh
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2008-08-19T00:00:00Z
full work available at URL: https://eudml.org/doc/55138
review text: Summary: Given an arbitrary measure \(\mu \), this study shows that the set of norm attaining multilinear forms is not dense in the space of all continuous multilinear forms on \(L_{1}(\mu )\). However, we have the density if and only if \(\mu \) is purely atomic. Furthermore, the study presents an example of a Banach space \(X\) in which the set of norm attaining operators from \(X\) into \(X^{\ast }\) is dense in the space of all bounded linear operators \(L(X,X^{\ast })\). In contrast, the set of norm attaining bilinear forms on \(X\) is not dense in the space of continuous bilinear forms on \(X\).
Mathematics Subject Classification ID: 46B04
Mathematics Subject Classification ID: 46G25
Mathematics Subject Classification ID: 47A07
zbMATH DE Number: 5313306
zbMATH Keywords: density
zbMATH Keywords: norm attaining operators
MaRDI profile type: Publication
OpenAlex ID: W2077529956
Wikidata QID: Q58645456
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DBLP publication ID: journals/ijmmsc/Saleh08
description: scientific article; zbMATH DE number 5313306