{"title":"广义Crofoot变换及其应用","authors":"Rewayat Khan, A. Farooq","doi":"10.1515/conop-2022-0138","DOIUrl":null,"url":null,"abstract":"Abstract Matrix-valued asymmetric truncated Toeplitz operators are compressions of multiplication operators acting between two model spaces. These are the generalization of matrix-valued truncated Toeplitz operators. In this article, we describe symbols of matrix-valued asymmetric truncated Toeplitz operators equal to the zero operator. We also use generalized Crofoot transform to find a connection between the symbols of matrix-valued asymmetric truncated Toeplitz operators T ( Θ 1 , Θ 2 ) {\\mathcal{T}}\\left({\\Theta }_{1},{\\Theta }_{2}) and T ( Θ 1 ′ , Θ 2 ′ ) {\\mathcal{T}}\\left({\\Theta }_{1}^{^{\\prime} },{\\Theta }_{2}^{^{\\prime} }) .","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Generalized Crofoot transform and applications\",\"authors\":\"Rewayat Khan, A. Farooq\",\"doi\":\"10.1515/conop-2022-0138\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Matrix-valued asymmetric truncated Toeplitz operators are compressions of multiplication operators acting between two model spaces. These are the generalization of matrix-valued truncated Toeplitz operators. In this article, we describe symbols of matrix-valued asymmetric truncated Toeplitz operators equal to the zero operator. We also use generalized Crofoot transform to find a connection between the symbols of matrix-valued asymmetric truncated Toeplitz operators T ( Θ 1 , Θ 2 ) {\\\\mathcal{T}}\\\\left({\\\\Theta }_{1},{\\\\Theta }_{2}) and T ( Θ 1 ′ , Θ 2 ′ ) {\\\\mathcal{T}}\\\\left({\\\\Theta }_{1}^{^{\\\\prime} },{\\\\Theta }_{2}^{^{\\\\prime} }) .\",\"PeriodicalId\":53800,\"journal\":{\"name\":\"Concrete Operators\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Concrete Operators\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/conop-2022-0138\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Concrete Operators","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/conop-2022-0138","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Abstract Matrix-valued asymmetric truncated Toeplitz operators are compressions of multiplication operators acting between two model spaces. These are the generalization of matrix-valued truncated Toeplitz operators. In this article, we describe symbols of matrix-valued asymmetric truncated Toeplitz operators equal to the zero operator. We also use generalized Crofoot transform to find a connection between the symbols of matrix-valued asymmetric truncated Toeplitz operators T ( Θ 1 , Θ 2 ) {\mathcal{T}}\left({\Theta }_{1},{\Theta }_{2}) and T ( Θ 1 ′ , Θ 2 ′ ) {\mathcal{T}}\left({\Theta }_{1}^{^{\prime} },{\Theta }_{2}^{^{\prime} }) .