{"title":"The BSE Property for Vector-Valued Frechet Lipschitz Algebras","authors":"A. Rejali, Maryam Aghakoochaki","doi":"10.28924/apjm/9-13","DOIUrl":null,"url":null,"abstract":"Let (X, d) be a metric space with at least two elements and (A, pl) be a commutative semisimple Frechet algebra over the scalar field C. The correlation between the BSE-property of the Frechet algebra (A, pl) and Lipd(X,A) is assessed. It is found and approved that if Lipd(X,A) is a BSEFrechet algebra, then so is A. The opposite correlation will hold if (A, pl) is unital.","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asia Pacific Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.28924/apjm/9-13","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
Let (X, d) be a metric space with at least two elements and (A, pl) be a commutative semisimple Frechet algebra over the scalar field C. The correlation between the BSE-property of the Frechet algebra (A, pl) and Lipd(X,A) is assessed. It is found and approved that if Lipd(X,A) is a BSEFrechet algebra, then so is A. The opposite correlation will hold if (A, pl) is unital.
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