韦伯定理的一些变体

Mathematical Proceedings of the Royal Irish Academy Pub Date : 1900-01-01 DOI:10.3318/PRIA.2004.104.1.67

S. Mécheri

{"title":"韦伯定理的一些变体","authors":"S. Mécheri","doi":"10.3318/PRIA.2004.104.1.67","DOIUrl":null,"url":null,"abstract":"Weber’s theorem says that if A : H 0 H is bounded and linear on a separable Hilbert space, then any operator that is compact, commutes with A and lies in the weak closure of the range of the inner derivation induced by A must also be quasinilpotent. In this note we consider related problems for generalised inner derivations associated with operators A and B on H.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"SOME VARIANTS OF WEBER'S THEOREM\",\"authors\":\"S. Mécheri\",\"doi\":\"10.3318/PRIA.2004.104.1.67\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Weber’s theorem says that if A : H 0 H is bounded and linear on a separable Hilbert space, then any operator that is compact, commutes with A and lies in the weak closure of the range of the inner derivation induced by A must also be quasinilpotent. In this note we consider related problems for generalised inner derivations associated with operators A and B on H.\",\"PeriodicalId\":434988,\"journal\":{\"name\":\"Mathematical Proceedings of the Royal Irish Academy\",\"volume\":\"16 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Proceedings of the Royal Irish Academy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3318/PRIA.2004.104.1.67\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Royal Irish Academy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3318/PRIA.2004.104.1.67","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 4

摘要

韦伯定理指出，如果A: H 0 H在可分离的希尔伯特空间上是有界线性的，那么任何紧的、与A交换的、位于由A引出的内导数范围的弱闭包内的算子也一定是拟无效的。本文考虑了H上与A和B算子相关的广义内导的相关问题。

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

SOME VARIANTS OF WEBER'S THEOREM

Weber’s theorem says that if A : H 0 H is bounded and linear on a separable Hilbert space, then any operator that is compact, commutes with A and lies in the weak closure of the range of the inner derivation induced by A must also be quasinilpotent. In this note we consider related problems for generalised inner derivations associated with operators A and B on H.

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

Mathematical Proceedings of the Royal Irish Academy

自引率

0.00%

发文量