论核算子特征值的分布

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2024-10-14 DOI:10.1134/S0016266324030109

Oleg Reinov

{"title":"论核算子特征值的分布","authors":"Oleg Reinov","doi":"10.1134/S0016266324030109","DOIUrl":null,"url":null,"abstract":"<p> It is shown how certain recent results in the theory of determinants and traces can be applied to obtain new theorems on the distribution of eigenvalues of nuclear operators on Banach spaces and to prove the equality of the spectral and nuclear traces of such operators. As an example, we consider a new class of operators: the class of generalized Lapresté nuclear operators. </p>","PeriodicalId":575,"journal":{"name":"Functional Analysis and Its Applications","volume":"58 3","pages":"344 - 346"},"PeriodicalIF":0.6000,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Distribution of Eigenvalues of Nuclear Operators\",\"authors\":\"Oleg Reinov\",\"doi\":\"10.1134/S0016266324030109\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> It is shown how certain recent results in the theory of determinants and traces can be applied to obtain new theorems on the distribution of eigenvalues of nuclear operators on Banach spaces and to prove the equality of the spectral and nuclear traces of such operators. As an example, we consider a new class of operators: the class of generalized Lapresté nuclear operators. </p>\",\"PeriodicalId\":575,\"journal\":{\"name\":\"Functional Analysis and Its Applications\",\"volume\":\"58 3\",\"pages\":\"344 - 346\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-10-14\",\"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/S0016266324030109\",\"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/S0016266324030109","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

本文展示了如何应用行列式和迹理论中的某些最新成果，获得关于巴拿赫空间上核算子特征值分布的新定理，并证明此类算子的谱迹和核迹相等。例如，我们考虑一类新的算子：广义拉普斯特核算子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the Distribution of Eigenvalues of Nuclear Operators

It is shown how certain recent results in the theory of determinants and traces can be applied to obtain new theorems on the distribution of eigenvalues of nuclear operators on Banach spaces and to prove the equality of the spectral and nuclear traces of such operators. As an example, we consider a new class of operators: the class of generalized Lapresté nuclear operators.

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.