还原组 $C^*$ 算法的理想分离特性

Are Austad, Hannes Thiel
{"title":"还原组 $C^*$ 算法的理想分离特性","authors":"Are Austad, Hannes Thiel","doi":"arxiv-2408.14880","DOIUrl":null,"url":null,"abstract":"We say that an inclusion of a $*$-algebra $A$ into a $C^*$-algebra $B$ has\nthe ideal separation property if closed ideals in $B$ can be recovered by their\nintersection with $A$. Such inclusions have attractive properties from the\npoint of view of harmonic analysis and noncommutative geometry. We establish\nseveral permanence properties of locally compact groups for which $L^1(G)\n\\subseteq C^*_{\\mathrm{red}}(G)$ has the ideal separation property.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The ideal separation property for reduced group $C^*$-algebras\",\"authors\":\"Are Austad, Hannes Thiel\",\"doi\":\"arxiv-2408.14880\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We say that an inclusion of a $*$-algebra $A$ into a $C^*$-algebra $B$ has\\nthe ideal separation property if closed ideals in $B$ can be recovered by their\\nintersection with $A$. Such inclusions have attractive properties from the\\npoint of view of harmonic analysis and noncommutative geometry. We establish\\nseveral permanence properties of locally compact groups for which $L^1(G)\\n\\\\subseteq C^*_{\\\\mathrm{red}}(G)$ has the ideal separation property.\",\"PeriodicalId\":501114,\"journal\":{\"name\":\"arXiv - MATH - Operator Algebras\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Operator Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.14880\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.14880","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

如果 $B$ 中的封闭理想可以通过它们与 $A$ 的交集恢复,我们就说 $*$-algebra $A$ 对 $C^*$-algebra $B$ 的包含具有理想分离性质。从谐波分析和非交换几何的角度来看,这种夹杂具有诱人的性质。我们建立了局部紧凑群的多个永久性质,其中 $L^1(G)\subseteq C^*_{\mathrm{red}}(G)$ 具有理想分离性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The ideal separation property for reduced group $C^*$-algebras
We say that an inclusion of a $*$-algebra $A$ into a $C^*$-algebra $B$ has the ideal separation property if closed ideals in $B$ can be recovered by their intersection with $A$. Such inclusions have attractive properties from the point of view of harmonic analysis and noncommutative geometry. We establish several permanence properties of locally compact groups for which $L^1(G) \subseteq C^*_{\mathrm{red}}(G)$ has the ideal separation property.
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
自引率
0.00%
发文量
0
×
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