{"title":"The Mazur–Ulam property for uniform algebras","authors":"O. Hatori","doi":"10.4064/sm210703-11-9","DOIUrl":null,"url":null,"abstract":"We give a sufficient condition for a Banach space with which the homogeneous extension of a surjective isometry from the unit sphere of it onto another one is real-linear. The condition is satisfied by a uniform algebra and a certain extremely $C$-regular space of real-valued continuous functions.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/sm210703-11-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 10
Abstract
We give a sufficient condition for a Banach space with which the homogeneous extension of a surjective isometry from the unit sphere of it onto another one is real-linear. The condition is satisfied by a uniform algebra and a certain extremely $C$-regular space of real-valued continuous functions.
期刊介绍：
The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.
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