赋范线性空间中弱紧集的凸性

IF 1.5 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI:10.1134/S1061920825600539

I.G. Tsar’kov

{"title":"赋范线性空间中弱紧集的凸性","authors":"I.G. Tsar’kov","doi":"10.1134/S1061920825600539","DOIUrl":null,"url":null,"abstract":" We study weakly compact subsets of normed linear spaces admitting, for each \\(\\varepsilon>0\\), an nw-continuous \\(\\varepsilon\\)-selection and such that the closure of their convex hull is weakly compact in this space. Such sets are shown to be convex. An application of this result to the linear manifold of all analytic functions in \\(L_1\\) is given. DOI 10.1134/S1061920825600539 ","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 3","pages":"585 - 589"},"PeriodicalIF":1.5000,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Convexity of Weakly Compact Sets in Normed Linear Spaces\",\"authors\":\"I.G. Tsar’kov\",\"doi\":\"10.1134/S1061920825600539\",\"DOIUrl\":null,\"url\":null,\"abstract\":\" We study weakly compact subsets of normed linear spaces admitting, for each \\\\(\\\\varepsilon>0\\\\), an nw-continuous \\\\(\\\\varepsilon\\\\)-selection and such that the closure of their convex hull is weakly compact in this space. Such sets are shown to be convex. An application of this result to the linear manifold of all analytic functions in \\\\(L_1\\\\) is given. DOI 10.1134/S1061920825600539 \",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":\"32 3\",\"pages\":\"585 - 589\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2025-09-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1061920825600539\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920825600539","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

我们研究赋范线性空间的弱紧子集，对于每个\(\varepsilon>0\)，允许一个nw连续的\(\varepsilon\) -选择，并且使得它们的凸包的闭包在这个空间中是弱紧的。这样的集合被证明是凸的。给出了该结果在\(L_1\)中所有解析函数的线性流形中的一个应用。Doi 10.1134/ s1061920825600539

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Convexity of Weakly Compact Sets in Normed Linear Spaces

We study weakly compact subsets of normed linear spaces admitting, for each \(\varepsilon>0\), an nw-continuous \(\varepsilon\)-selection and such that the closure of their convex hull is weakly compact in this space. Such sets are shown to be convex. An application of this result to the linear manifold of all analytic functions in \(L_1\) is given.

DOI 10.1134/S1061920825600539

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.