Alexander Caicedo, J. Ramos-Fernández, M. Salas-Brown
{"title":"On the compactness and the essential norm of operators defined by infinite tridiagonal matrices","authors":"Alexander Caicedo, J. Ramos-Fernández, M. Salas-Brown","doi":"10.1515/conop-2022-0143","DOIUrl":null,"url":null,"abstract":"Abstract In this article, all sequences u {\\boldsymbol{u}} , v {\\boldsymbol{v}} , and w {\\boldsymbol{w}} that define continuous and compact tridiagonal operators T u , v , w {T}_{u,v,w} acting on the weighted sequence space l β 2 {l}_{\\beta }^{2} were characterized. Additionally, the essential norm of this operator, and as an important consequence of our results, the essential norm of multiplication operator M u {M}_{u} acting on l β 2 {l}_{\\beta }^{2} spaces was calculated.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":"10 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Concrete Operators","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/conop-2022-0143","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract In this article, all sequences u {\boldsymbol{u}} , v {\boldsymbol{v}} , and w {\boldsymbol{w}} that define continuous and compact tridiagonal operators T u , v , w {T}_{u,v,w} acting on the weighted sequence space l β 2 {l}_{\beta }^{2} were characterized. Additionally, the essential norm of this operator, and as an important consequence of our results, the essential norm of multiplication operator M u {M}_{u} acting on l β 2 {l}_{\beta }^{2} spaces was calculated.
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