Norm attaining operators and variational principle

IF 0.7 3区 数学 Q2 MATHEMATICS
M. Bachir
{"title":"Norm attaining operators and variational principle","authors":"M. Bachir","doi":"10.4064/sm210628-6-9","DOIUrl":null,"url":null,"abstract":". We establish a linear variational principle extending Deville–Godefroy– Zizler’s one. We use this variational principle to prove that if X is a Banach space having property ( α ) of Schachermayer and Y is any Banach space, then the set of all strongly norm attaining linear operators from X into Y is the complement of a σ -porous set. Moreover, we apply our results to an abstract class of (linear and nonlinear) operator spaces.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/sm210628-6-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3

Abstract

. We establish a linear variational principle extending Deville–Godefroy– Zizler’s one. We use this variational principle to prove that if X is a Banach space having property ( α ) of Schachermayer and Y is any Banach space, then the set of all strongly norm attaining linear operators from X into Y is the complement of a σ -porous set. Moreover, we apply our results to an abstract class of (linear and nonlinear) operator spaces.
求范数算子与变分原理
.我们建立了一个线性变分原理,推广了Deville–Godefroy–Zizler的变分原理。我们用这个变分原理证明了如果X是一个具有Schachermayer性质(α)的Banach空间,并且Y是任何Banach空间时,则从X到Y的所有强范数线性算子的集合是σ-多孔集合的补集。此外,我们将我们的结果应用于一类抽象的(线性和非线性)算子空间。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Studia Mathematica
Studia Mathematica 数学-数学
CiteScore
1.50
自引率
12.50%
发文量
72
审稿时长
5 months
期刊介绍: The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信