{"title":"Commutativity and Compactness of kth Order Slant Toeplitz Operators","authors":"M. Premjit Singh, Khumballambam Priyobarta Singh, Elija Chongtham, Oinam Nilbir Singh","doi":"10.1007/s11785-024-01570-w","DOIUrl":null,"url":null,"abstract":"<p>In this paper, commutativity of the compressions of <i>k</i>th order slant Toeplitz operators is discussed. We show that the commutativity and essential commutativity of two compressions of <i>k</i>th order slant Toeplitz operators on <span>\\(H^2\\)</span> are same. We also establish some results on the compactness of the compressions of <i>k</i>th order slant Toeplitz operators. In the last section, we discuss various similarities and differences between compactness and non-compactness of these operators by simply looking at their graphs.\n</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"19 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex Analysis and Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11785-024-01570-w","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, commutativity of the compressions of kth order slant Toeplitz operators is discussed. We show that the commutativity and essential commutativity of two compressions of kth order slant Toeplitz operators on \(H^2\) are same. We also establish some results on the compactness of the compressions of kth order slant Toeplitz operators. In the last section, we discuss various similarities and differences between compactness and non-compactness of these operators by simply looking at their graphs.
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Complex Analysis and Operator Theory (CAOT) is devoted to the publication of current research developments in the closely related fields of complex analysis and operator theory as well as in applications to system theory, harmonic analysis, probability, statistics, learning theory, mathematical physics and other related fields. Articles using the theory of reproducing kernel spaces are in particular welcomed.
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