{"title":"Decomposition in direct sum of seminormed vector spaces and Mazur–Ulam theorem","authors":"Oleksiy Dovgoshey, Jürgen Prestin, Igor Shevchuk","doi":"10.1515/ms-2024-0010","DOIUrl":null,"url":null,"abstract":"It was proved by S. Mazur and S. Ulam in 1932 that every isometric surjection between normed real vector spaces is affine. We generalize the Mazur–Ulam theorem and find necessary and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"18 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Slovaca","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ms-2024-0010","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: 0
Abstract
It was proved by S. Mazur and S. Ulam in 1932 that every isometric surjection between normed real vector spaces is affine. We generalize the Mazur–Ulam theorem and find necessary and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear.
期刊介绍：
Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc. The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.
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
