{"title":"一些具有仿射符号的 2×2 块托普利兹算子通过包络的数值范围","authors":"Linda J. Patton, Brooke Randell","doi":"10.1007/s43036-024-00395-w","DOIUrl":null,"url":null,"abstract":"<div><p>The envelope algorithm is used to precisely describe the numerical range of a block Toeplitz operator with 2-by-2 affine symbol in the case where the numerical range of the symbol at each point of the unit circle is a circular disk. In this setting, there is at most one flat portion on the boundary of the numerical range. Necessary and sufficient conditions are given for the flat portion to materialize.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00395-w.pdf","citationCount":"0","resultStr":"{\"title\":\"Numerical ranges of some 2-by-2 block Toeplitz operators with affine symbols via envelopes\",\"authors\":\"Linda J. Patton, Brooke Randell\",\"doi\":\"10.1007/s43036-024-00395-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The envelope algorithm is used to precisely describe the numerical range of a block Toeplitz operator with 2-by-2 affine symbol in the case where the numerical range of the symbol at each point of the unit circle is a circular disk. In this setting, there is at most one flat portion on the boundary of the numerical range. Necessary and sufficient conditions are given for the flat portion to materialize.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-10-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s43036-024-00395-w.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-024-00395-w\",\"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/s43036-024-00395-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Numerical ranges of some 2-by-2 block Toeplitz operators with affine symbols via envelopes
The envelope algorithm is used to precisely describe the numerical range of a block Toeplitz operator with 2-by-2 affine symbol in the case where the numerical range of the symbol at each point of the unit circle is a circular disk. In this setting, there is at most one flat portion on the boundary of the numerical range. Necessary and sufficient conditions are given for the flat portion to materialize.
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