{"title":"圆盘代数和哈代空间中的广义塞萨罗算子","authors":"Angela A. Albanese, José Bonet, Werner J. Ricker","doi":"10.1007/s43036-024-00396-9","DOIUrl":null,"url":null,"abstract":"<div><p>Generalized Cesàro operators <span>\\(C_t\\)</span>, for <span>\\(t\\in [0,1)\\)</span>, are investigated when they act on the disc algebra <span>\\(A({\\mathbb {D}})\\)</span> and on the Hardy spaces <span>\\(H^p\\)</span>, for <span>\\(1\\le p \\le \\infty \\)</span>. We study the continuity, compactness, spectrum and point spectrum of <span>\\(C_t\\)</span> as well as their linear dynamics and mean ergodicity on these spaces.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00396-9.pdf","citationCount":"0","resultStr":"{\"title\":\"Generalized Cesàro operators in the disc algebra and in Hardy spaces\",\"authors\":\"Angela A. Albanese, José Bonet, Werner J. Ricker\",\"doi\":\"10.1007/s43036-024-00396-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Generalized Cesàro operators <span>\\\\(C_t\\\\)</span>, for <span>\\\\(t\\\\in [0,1)\\\\)</span>, are investigated when they act on the disc algebra <span>\\\\(A({\\\\mathbb {D}})\\\\)</span> and on the Hardy spaces <span>\\\\(H^p\\\\)</span>, for <span>\\\\(1\\\\le p \\\\le \\\\infty \\\\)</span>. We study the continuity, compactness, spectrum and point spectrum of <span>\\\\(C_t\\\\)</span> as well as their linear dynamics and mean ergodicity on these spaces.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-10-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s43036-024-00396-9.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-024-00396-9\",\"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/s43036-024-00396-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Generalized Cesàro operators in the disc algebra and in Hardy spaces
Generalized Cesàro operators \(C_t\), for \(t\in [0,1)\), are investigated when they act on the disc algebra \(A({\mathbb {D}})\) and on the Hardy spaces \(H^p\), for \(1\le p \le \infty \). We study the continuity, compactness, spectrum and point spectrum of \(C_t\) as well as their linear dynamics and mean ergodicity on these spaces.
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