成对核和截断的Toeplitz运算符

IF 0.7 Q2 MATHEMATICS Advances in Operator Theory Pub Date : 2025-02-27 DOI:10.1007/s43036-025-00426-0

M. Cristina Câmara, Jonathan R. Partington

{"title":"成对核和截断的Toeplitz运算符","authors":"M. Cristina Câmara, Jonathan R. Partington","doi":"10.1007/s43036-025-00426-0","DOIUrl":null,"url":null,"abstract":"<div><p>This paper considers paired operators in the context of the Lebesgue Hilbert space <span>\\(L^2\\)</span> on the unit circle and its subspace, the Hardy space <span>\\(H^2.\\)</span> The kernels of such operators, together with their analytic projections, which are generalizations of Toeplitz kernels, are studied. Inclusion relations between such kernels are considered in detail, and the results are applied to describing the kernels of finite-rank asymmetric truncated Toeplitz operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00426-0.pdf","citationCount":"0","resultStr":"{\"title\":\"Paired kernels and truncated Toeplitz operators\",\"authors\":\"M. Cristina Câmara, Jonathan R. Partington\",\"doi\":\"10.1007/s43036-025-00426-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper considers paired operators in the context of the Lebesgue Hilbert space <span>\\\\(L^2\\\\)</span> on the unit circle and its subspace, the Hardy space <span>\\\\(H^2.\\\\)</span> The kernels of such operators, together with their analytic projections, which are generalizations of Toeplitz kernels, are studied. Inclusion relations between such kernels are considered in detail, and the results are applied to describing the kernels of finite-rank asymmetric truncated Toeplitz operators.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"10 2\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-02-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s43036-025-00426-0.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-025-00426-0\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-025-00426-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了单位圆上的Lebesgue Hilbert空间\(L^2\)及其子空间Hardy空间\(H^2.\)上的配对算子，研究了这类算子的核及其解析投影，即Toeplitz核的推广。详细考虑了这些核之间的包含关系，并将结果应用于有限秩非对称截断Toeplitz算子核的描述。

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

Paired kernels and truncated Toeplitz operators

This paper considers paired operators in the context of the Lebesgue Hilbert space \(L^2\) on the unit circle and its subspace, the Hardy space \(H^2.\) The kernels of such operators, together with their analytic projections, which are generalizations of Toeplitz kernels, are studied. Inclusion relations between such kernels are considered in detail, and the results are applied to describing the kernels of finite-rank asymmetric truncated Toeplitz 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