{"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}
引用次数: 0
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.