某些向量值巴拿赫函数代数的 BSE 特性

IF 1.2 4区 数学 Q1 MATHEMATICS Acta Mathematica Scientia Pub Date : 2024-08-27 DOI:10.1007/s10473-024-0518-z
Fatemeh Abtahi, Ali Rejali, Farshad Sayaf
{"title":"某些向量值巴拿赫函数代数的 BSE 特性","authors":"Fatemeh Abtahi, Ali Rejali, Farshad Sayaf","doi":"10.1007/s10473-024-0518-z","DOIUrl":null,"url":null,"abstract":"<p>In this paper, <i>X</i> is a locally compact Hausdorff space and <span>\\({\\cal A}\\)</span> is a Banach algebra. First, we study some basic features of <i>C</i><sub>0</sub>(<i>X</i>, <span>\\({\\cal A}\\)</span>) related to BSE concept, which are gotten from <span>\\({\\cal A}\\)</span>. In particular, we prove that if <i>C</i><sub>0</sub>(<i>X</i>, <span>\\({\\cal A}\\)</span>) has the BSE property then <span>\\({\\cal A}\\)</span> has so. We also establish the converse of this result, whenever <i>X</i> is discrete and <span>\\({\\cal A}\\)</span> has the BSE-norm property. Furthermore, we prove the same result for the BSE property of type I. Finally, we prove that <i>C</i><sub>0</sub> (<i>X</i>, <span>\\({\\cal A}\\)</span>) has the BSE-norm property if and only if <span>\\({\\cal A}\\)</span> has so.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The BSE property for some vector-valued Banach function algebras\",\"authors\":\"Fatemeh Abtahi, Ali Rejali, Farshad Sayaf\",\"doi\":\"10.1007/s10473-024-0518-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, <i>X</i> is a locally compact Hausdorff space and <span>\\\\({\\\\cal A}\\\\)</span> is a Banach algebra. First, we study some basic features of <i>C</i><sub>0</sub>(<i>X</i>, <span>\\\\({\\\\cal A}\\\\)</span>) related to BSE concept, which are gotten from <span>\\\\({\\\\cal A}\\\\)</span>. In particular, we prove that if <i>C</i><sub>0</sub>(<i>X</i>, <span>\\\\({\\\\cal A}\\\\)</span>) has the BSE property then <span>\\\\({\\\\cal A}\\\\)</span> has so. We also establish the converse of this result, whenever <i>X</i> is discrete and <span>\\\\({\\\\cal A}\\\\)</span> has the BSE-norm property. Furthermore, we prove the same result for the BSE property of type I. Finally, we prove that <i>C</i><sub>0</sub> (<i>X</i>, <span>\\\\({\\\\cal A}\\\\)</span>) has the BSE-norm property if and only if <span>\\\\({\\\\cal A}\\\\)</span> has so.</p>\",\"PeriodicalId\":50998,\"journal\":{\"name\":\"Acta Mathematica Scientia\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Scientia\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10473-024-0518-z\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Scientia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10473-024-0518-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

在本文中,X 是局部紧凑的 Hausdorff 空间,\({\cal A}\) 是一个巴拿赫代数。首先,我们研究了 C0(X, \({\cal A}\)) 与 BSE 概念相关的一些基本特征,这些特征是从 \({\cal A}\) 中得到的。特别是,我们证明如果 C0(X, \({\cal A}\)) 具有 BSE 属性,那么 \({\cal A}\) 也具有 BSE 属性。只要 X 是离散的,并且 \({\cal A}\) 具有 BSE 规范属性,我们也会建立这个结果的反面。最后,我们证明当且仅当\({\cal A}\)具有BSE-norm性质时,C0 (X, \({\cal A}\))才具有BSE-norm性质。
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
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
The BSE property for some vector-valued Banach function algebras

In this paper, X is a locally compact Hausdorff space and \({\cal A}\) is a Banach algebra. First, we study some basic features of C0(X, \({\cal A}\)) related to BSE concept, which are gotten from \({\cal A}\). In particular, we prove that if C0(X, \({\cal A}\)) has the BSE property then \({\cal A}\) has so. We also establish the converse of this result, whenever X is discrete and \({\cal A}\) has the BSE-norm property. Furthermore, we prove the same result for the BSE property of type I. Finally, we prove that C0 (X, \({\cal A}\)) has the BSE-norm property if and only if \({\cal A}\) has so.

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
CiteScore
2.00
自引率
10.00%
发文量
2614
审稿时长
6 months
期刊介绍: Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981. The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.
期刊最新文献
Lévy area analysis and parameter estimation for fOU processes via non-geometric rough path theory Heat kernel on Ricci shrinkers (II) Variational analysis for the maximal time function in normed spaces Toeplitz operators between weighted Bergman spaces over the half-plane Global unique solutions for the incompressible MHD equations with variable density and electrical conductivity
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1