四元克雷因空间数值范围的频谱包容特性

IF 0.6 4区数学 Q3 MATHEMATICS Functional Analysis and Its Applications Pub Date : 2024-04-30 DOI:10.1134/S0016266323050027

Kamel Mahfoudhi

{"title":"四元克雷因空间数值范围的频谱包容特性","authors":"Kamel Mahfoudhi","doi":"10.1134/S0016266323050027","DOIUrl":null,"url":null,"abstract":" The article provides a concise overview of key concepts related to right quaternionic linear operators, quaternionic Hilbert spaces, and quaternionic Krein spaces. It then delves into the study of the quaternionic Krein space numerical range of a bounded right linear operator and the relationship between this numerical range and the \\(S\\)-spectrum of the operator. The article concludes by establishing spectral inclusion results based on the quaternionic Krein space numerical range and presenting the corresponding spectral inclusion theorems. In addition, we generalize some results to infinite dimensional quaternionic Krein spaces and give some examples. ","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"57 1 supplement","pages":"17 - 25"},"PeriodicalIF":0.6000,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Spectral Inclusion Properties of Quaternionic Krein Space Numerical Range\",\"authors\":\"Kamel Mahfoudhi\",\"doi\":\"10.1134/S0016266323050027\",\"DOIUrl\":null,\"url\":null,\"abstract\":\" The article provides a concise overview of key concepts related to right quaternionic linear operators, quaternionic Hilbert spaces, and quaternionic Krein spaces. It then delves into the study of the quaternionic Krein space numerical range of a bounded right linear operator and the relationship between this numerical range and the \\\\(S\\\\)-spectrum of the operator. The article concludes by establishing spectral inclusion results based on the quaternionic Krein space numerical range and presenting the corresponding spectral inclusion theorems. In addition, we generalize some results to infinite dimensional quaternionic Krein spaces and give some examples. \",\"PeriodicalId\":575,\"journal\":{\"name\":\"Functional Analysis and Its Applications\",\"volume\":\"57 1 supplement\",\"pages\":\"17 - 25\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Functional Analysis and Its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0016266323050027\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Functional Analysis and Its Applications","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S0016266323050027","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要文章简明扼要地概述了与右四元线性算子、四元希尔伯特空间和四元克雷因空间有关的关键概念。然后，文章深入研究了有界右线性算子的四元克雷因空间数值范围，以及该数值范围与算子的（S\）谱之间的关系。文章最后建立了基于四元克雷因空间数值范围的谱包含结果，并给出了相应的谱包含定理。此外，我们还将一些结果推广到无限维四元克雷因空间，并给出了一些例子。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Spectral Inclusion Properties of Quaternionic Krein Space Numerical Range

The article provides a concise overview of key concepts related to right quaternionic linear operators, quaternionic Hilbert spaces, and quaternionic Krein spaces. It then delves into the study of the quaternionic Krein space numerical range of a bounded right linear operator and the relationship between this numerical range and the \(S\)-spectrum of the operator. The article concludes by establishing spectral inclusion results based on the quaternionic Krein space numerical range and presenting the corresponding spectral inclusion theorems. In addition, we generalize some results to infinite dimensional quaternionic Krein spaces and give some examples.

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

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.