{"title":"有限维Banach空间正锥上$\\varepsilon$-等距的稳定性","authors":"Longfa Sun, Ya-jing Ma","doi":"10.36045/j.bbms.200413","DOIUrl":null,"url":null,"abstract":"A weak stability bound for the $\\varepsilon$-isometry $f$ form the positive cone of a reflexive, strictly convex and Gateaux smooth Banach lattice $X$ to a Banach space $Y$ is presented. This result is used to prove the stability theorem for the $\\varepsilon$-isometry $f:(\\mathbb{R}^n)^+\\rightarrow Y$, where $\\mathbb{R}^n$ is the $n$-dimensional space equipped with a $1$-unconditional norm and $Y$ is a n-dimensional, strictly convex and Gateaux smooth space.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability of $\\\\varepsilon$-isometries on the positive cones of finite-dimensional Banach spaces\",\"authors\":\"Longfa Sun, Ya-jing Ma\",\"doi\":\"10.36045/j.bbms.200413\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A weak stability bound for the $\\\\varepsilon$-isometry $f$ form the positive cone of a reflexive, strictly convex and Gateaux smooth Banach lattice $X$ to a Banach space $Y$ is presented. This result is used to prove the stability theorem for the $\\\\varepsilon$-isometry $f:(\\\\mathbb{R}^n)^+\\\\rightarrow Y$, where $\\\\mathbb{R}^n$ is the $n$-dimensional space equipped with a $1$-unconditional norm and $Y$ is a n-dimensional, strictly convex and Gateaux smooth space.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.36045/j.bbms.200413\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.36045/j.bbms.200413","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Stability of $\varepsilon$-isometries on the positive cones of finite-dimensional Banach spaces
A weak stability bound for the $\varepsilon$-isometry $f$ form the positive cone of a reflexive, strictly convex and Gateaux smooth Banach lattice $X$ to a Banach space $Y$ is presented. This result is used to prove the stability theorem for the $\varepsilon$-isometry $f:(\mathbb{R}^n)^+\rightarrow Y$, where $\mathbb{R}^n$ is the $n$-dimensional space equipped with a $1$-unconditional norm and $Y$ is a n-dimensional, strictly convex and Gateaux smooth space.