{"title":"$\\mathbb{C}上Fock空间上的二重和复对称加权复合算子$","authors":"C. Santhoshkumar","doi":"10.30970/ms.59.1.106-112","DOIUrl":null,"url":null,"abstract":"In this paper, we give simple characterization of binormal weighted composition operators $C_{\\psi, \\phi}$ on the Fock space over $\\mathbb{C}$ where weight function is of the form $\\psi(\\zeta) = e^{\\langle \\zeta, c \\rangle}$ for some $c \\in \\mathbb{C}$. We derive conditions for $C_{\\phi}$ to be binormal such that $C^*_{\\phi}C_{\\phi}$ and $C^*_{\\phi} + C_{\\phi}$ commute. Finally we give some simple characterization of binormal weighted composition operator to be complex symmetric.","PeriodicalId":37555,"journal":{"name":"Matematychni Studii","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Binormal and complex symmetric weighted composition operators on the Fock Space over $\\\\mathbb{C}$\",\"authors\":\"C. Santhoshkumar\",\"doi\":\"10.30970/ms.59.1.106-112\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we give simple characterization of binormal weighted composition operators $C_{\\\\psi, \\\\phi}$ on the Fock space over $\\\\mathbb{C}$ where weight function is of the form $\\\\psi(\\\\zeta) = e^{\\\\langle \\\\zeta, c \\\\rangle}$ for some $c \\\\in \\\\mathbb{C}$. We derive conditions for $C_{\\\\phi}$ to be binormal such that $C^*_{\\\\phi}C_{\\\\phi}$ and $C^*_{\\\\phi} + C_{\\\\phi}$ commute. Finally we give some simple characterization of binormal weighted composition operator to be complex symmetric.\",\"PeriodicalId\":37555,\"journal\":{\"name\":\"Matematychni Studii\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-03-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Matematychni Studii\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30970/ms.59.1.106-112\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matematychni Studii","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30970/ms.59.1.106-112","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Binormal and complex symmetric weighted composition operators on the Fock Space over $\mathbb{C}$
In this paper, we give simple characterization of binormal weighted composition operators $C_{\psi, \phi}$ on the Fock space over $\mathbb{C}$ where weight function is of the form $\psi(\zeta) = e^{\langle \zeta, c \rangle}$ for some $c \in \mathbb{C}$. We derive conditions for $C_{\phi}$ to be binormal such that $C^*_{\phi}C_{\phi}$ and $C^*_{\phi} + C_{\phi}$ commute. Finally we give some simple characterization of binormal weighted composition operator to be complex symmetric.