{"title":"Controlled Frames in n-Hilbert Spaces and Their Tensor Products","authors":"P. Ghosh, T. K. Samanta","doi":"10.3103/s1066369x24700312","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The concepts of controlled frame and it’s dual in <span>\\(n\\)</span>-Hilbert space have been introduced and then some of their properties are going to be discussed. Also, we study controlled frame in tensor product of <span>\\(n\\)</span>-Hilbert spaces and establish a relationship between controlled frame and bounded linear operator in tensor product of <span>\\(n\\)</span>-Hilbert spaces. At the end, we consider the direct sum of controlled frames in <span>\\(n\\)</span>-Hilbert space.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"65 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1066369x24700312","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
The concepts of controlled frame and it’s dual in \(n\)-Hilbert space have been introduced and then some of their properties are going to be discussed. Also, we study controlled frame in tensor product of \(n\)-Hilbert spaces and establish a relationship between controlled frame and bounded linear operator in tensor product of \(n\)-Hilbert spaces. At the end, we consider the direct sum of controlled frames in \(n\)-Hilbert space.
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