{"title":"ON BOUNDEDNESS WITH SPEED λ IN ULTRAMETRIC FIELDS","authors":"Natarajan Narayanasubramanian Pinnangudi","doi":"10.22190/fumi211031045p","DOIUrl":null,"url":null,"abstract":"In the present paper, K denotes a complete, non-trivially valued, ultrametric (or non-archimedean) field. Entries of sequences, infinite series and infinite matrices are in K. Following Kangro [2, 3, 4], we introduce the concept of boundedness with speed λ or λ-boundedness. We then obtain a characterization of the matrix class (mλ , mµ ), where mλ denotes the set of all λ-bounded sequences in K. We conclude the paper with a remark about the matrix class (c λ , mµ ), where c λ denotes the set of all λ-convergent sequences in K.","PeriodicalId":54148,"journal":{"name":"Facta Universitatis-Series Mathematics and Informatics","volume":"40 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Facta Universitatis-Series Mathematics and Informatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22190/fumi211031045p","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 the present paper, K denotes a complete, non-trivially valued, ultrametric (or non-archimedean) field. Entries of sequences, infinite series and infinite matrices are in K. Following Kangro [2, 3, 4], we introduce the concept of boundedness with speed λ or λ-boundedness. We then obtain a characterization of the matrix class (mλ , mµ ), where mλ denotes the set of all λ-bounded sequences in K. We conclude the paper with a remark about the matrix class (c λ , mµ ), where c λ denotes the set of all λ-convergent sequences in K.
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