算子对的Hilbert-Schmidt数值半径

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Acta Applicandae Mathematicae Pub Date : 2023-12-04 DOI:10.1007/s10440-023-00624-z

Soumia Aici, Abdelkader Frakis, Fuad Kittaneh

{"title":"算子对的Hilbert-Schmidt数值半径","authors":"Soumia Aici, Abdelkader Frakis, Fuad Kittaneh","doi":"10.1007/s10440-023-00624-z","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce a new norm on <span>\\(\\mathcal{C}_{2}\\times \\mathcal{C}_{2}\\)</span>, where <span>\\(\\mathcal{C}_{2}\\)</span> is the Hilbert-Schmidt class. We study basic properties of this norm and prove inequalities involving it. As an application of the present study, we deduce a chain of new bounds for the Hilbert-Schmidt numerical radii of <span>\\(2\\times 2\\)</span> operator matrices. Connection with the classical Hilbert-Schmidt numerical radius of a single operator are also provided. Moreover, we refine some related existing bounds, too.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hilbert-Schmidt Numerical Radius of a Pair of Operators\",\"authors\":\"Soumia Aici, Abdelkader Frakis, Fuad Kittaneh\",\"doi\":\"10.1007/s10440-023-00624-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We introduce a new norm on <span>\\\\(\\\\mathcal{C}_{2}\\\\times \\\\mathcal{C}_{2}\\\\)</span>, where <span>\\\\(\\\\mathcal{C}_{2}\\\\)</span> is the Hilbert-Schmidt class. We study basic properties of this norm and prove inequalities involving it. As an application of the present study, we deduce a chain of new bounds for the Hilbert-Schmidt numerical radii of <span>\\\\(2\\\\times 2\\\\)</span> operator matrices. Connection with the classical Hilbert-Schmidt numerical radius of a single operator are also provided. Moreover, we refine some related existing bounds, too.</p></div>\",\"PeriodicalId\":53132,\"journal\":{\"name\":\"Acta Applicandae Mathematicae\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-12-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Applicandae Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10440-023-00624-z\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Applicandae Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10440-023-00624-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

我们在 \(\mathcal{C}_{2}\times \mathcal{C}_{2}\) 上引入了一种新的规范，其中 \(\mathcal{C}_{2}\) 是希尔伯特-施密特类。我们研究了这一规范的基本性质，并证明了涉及它的不等式。作为本研究的一个应用，我们为 \(2\times 2\) 算子矩阵的希尔伯特-施密特数值半径推导出了一连串新的边界。我们还提供了与经典的单算子希尔伯特-施密特数值半径的联系。此外，我们还完善了一些相关的现有边界。

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

Hilbert-Schmidt Numerical Radius of a Pair of Operators

We introduce a new norm on \(\mathcal{C}_{2}\times \mathcal{C}_{2}\), where \(\mathcal{C}_{2}\) is the Hilbert-Schmidt class. We study basic properties of this norm and prove inequalities involving it. As an application of the present study, we deduce a chain of new bounds for the Hilbert-Schmidt numerical radii of \(2\times 2\) operator matrices. Connection with the classical Hilbert-Schmidt numerical radius of a single operator are also provided. Moreover, we refine some related existing bounds, too.

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

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.