{"title":"A study on q-analogue of Catalan sequence spaces","authors":"Taja Yaying, Merve Kara, B. Hazarika, E. Kara","doi":"10.2298/fil2303839y","DOIUrl":null,"url":null,"abstract":"In this study, we construct q-analog C(q) of Catalan matrix and study the sequence spaces c0(C(q)) and c(C(q)) defined as the domain of q-Catalan matrix C(q) in the spaces c0 and c, respectively. We exhibit some topological properties, obtain Schauder bases and determine ?-, ?-, and ?-duals of the spaces c0(C(q)) and c(C(q)). Finally, we characterize certain class of matrix mappings from the spaces c0(C(q)) and c(C(q)) to the space ? = {??, c0, c, ?1} and give the necessary and sufficient conditions for a matrix operator to be compact.","PeriodicalId":12305,"journal":{"name":"Filomat","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Filomat","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2298/fil2303839y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 5
Abstract
In this study, we construct q-analog C(q) of Catalan matrix and study the sequence spaces c0(C(q)) and c(C(q)) defined as the domain of q-Catalan matrix C(q) in the spaces c0 and c, respectively. We exhibit some topological properties, obtain Schauder bases and determine ?-, ?-, and ?-duals of the spaces c0(C(q)) and c(C(q)). Finally, we characterize certain class of matrix mappings from the spaces c0(C(q)) and c(C(q)) to the space ? = {??, c0, c, ?1} and give the necessary and sufficient conditions for a matrix operator to be compact.
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