{"title":"q 伯格曼空间上的托普利兹算子和组成算子","authors":"Houcine Sadraoui, Borhen Halouani","doi":"10.1007/s11868-023-00583-x","DOIUrl":null,"url":null,"abstract":"<p>In this work we consider Toeplitz operators and composition operators on the <i>q</i>-Bergman space.We give some spectral properties of Toeplitz operators in general and a sufficient condition for hyponormality of Toeplitz operators in the case of a symbol where the analytic part is a monomial. We also give a necessary condition for hyponormality in the general case of a harmonic symbol as well as a necessary and sufficient condition for such operators to commute. For composition operators we give necessary conditions and sufficient conditions for their compactness and normality, as well as necessary conditions for cohyponormality in the case of a linear fractional map and we finally compute the adjoint in the case of a linear map.\n</p>","PeriodicalId":48793,"journal":{"name":"Journal of Pseudo-Differential Operators and Applications","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Toeplitz operators and composition operators on the q-Bergman space\",\"authors\":\"Houcine Sadraoui, Borhen Halouani\",\"doi\":\"10.1007/s11868-023-00583-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this work we consider Toeplitz operators and composition operators on the <i>q</i>-Bergman space.We give some spectral properties of Toeplitz operators in general and a sufficient condition for hyponormality of Toeplitz operators in the case of a symbol where the analytic part is a monomial. We also give a necessary condition for hyponormality in the general case of a harmonic symbol as well as a necessary and sufficient condition for such operators to commute. For composition operators we give necessary conditions and sufficient conditions for their compactness and normality, as well as necessary conditions for cohyponormality in the case of a linear fractional map and we finally compute the adjoint in the case of a linear map.\\n</p>\",\"PeriodicalId\":48793,\"journal\":{\"name\":\"Journal of Pseudo-Differential Operators and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-02-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Pseudo-Differential Operators and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11868-023-00583-x\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pseudo-Differential Operators and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11868-023-00583-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Toeplitz operators and composition operators on the q-Bergman space
In this work we consider Toeplitz operators and composition operators on the q-Bergman space.We give some spectral properties of Toeplitz operators in general and a sufficient condition for hyponormality of Toeplitz operators in the case of a symbol where the analytic part is a monomial. We also give a necessary condition for hyponormality in the general case of a harmonic symbol as well as a necessary and sufficient condition for such operators to commute. For composition operators we give necessary conditions and sufficient conditions for their compactness and normality, as well as necessary conditions for cohyponormality in the case of a linear fractional map and we finally compute the adjoint in the case of a linear map.
期刊介绍：
The Journal of Pseudo-Differential Operators and Applications is a forum for high quality papers in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, functional analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and novel applications in engineering, geophysics and medical sciences.
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