{"title":"BSE PROPERTY OF FRÉCHET ALGEBRA","authors":"Ali Rejali, Mitra Amiri","doi":"10.1216/rmj.2023.53.1553","DOIUrl":null,"url":null,"abstract":"A class of commutative Banach algebras which satisfy a Bochner–Schoenberg–Eberlein-type inequality was introduced by Takahasi and Hatori. We generalize this property for the commutative Fréchet algebra (𝒜,pℓ)ℓ∈ℕ. Moreover, we verify and generalize some of the main results in the class of Banach algebras, for the Fréchet case. We prove that all Fréchet C*-algebras and also uniform Fréchet algebras are BSE algebras. Also, we show that C∞[0,1] is not a Fréchet BSE algebra.","PeriodicalId":49591,"journal":{"name":"Rocky Mountain Journal of Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rocky Mountain Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1216/rmj.2023.53.1553","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: 0
Abstract
A class of commutative Banach algebras which satisfy a Bochner–Schoenberg–Eberlein-type inequality was introduced by Takahasi and Hatori. We generalize this property for the commutative Fréchet algebra (𝒜,pℓ)ℓ∈ℕ. Moreover, we verify and generalize some of the main results in the class of Banach algebras, for the Fréchet case. We prove that all Fréchet C*-algebras and also uniform Fréchet algebras are BSE algebras. Also, we show that C∞[0,1] is not a Fréchet BSE algebra.
期刊介绍：
Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles.
The Rocky Mountain Journal of Mathematics endeavors to publish significant research papers and substantial expository/survey papers in a broad range of theoretical and applied areas of mathematics. For this reason the editorial board is broadly based and submissions are accepted in most areas of mathematics.
In addition, the journal publishes specialized conference proceedings.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
