{"title":"Spectral Inclusion Properties of Quaternionic Krein Space Numerical Range","authors":"Kamel Mahfoudhi","doi":"10.1134/S0016266323050027","DOIUrl":null,"url":null,"abstract":"<p> 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 <span>\\(S\\)</span>-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. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":null,"pages":null},"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}
引用次数: 0
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.
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.
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