有限维Banach空间正锥上$\varepsilon$-等距的稳定性

IF 0.4 4区数学 Q4 MATHEMATICS

Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2020-12-01 DOI:10.36045/j.bbms.200413

Longfa Sun, Ya-jing Ma

{"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":55309,"journal":{"name":"Bulletin of the Belgian Mathematical Society-Simon Stevin","volume":"1 1","pages":"789-800"},"PeriodicalIF":0.4000,"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\":55309,\"journal\":{\"name\":\"Bulletin of the Belgian Mathematical Society-Simon Stevin\",\"volume\":\"1 1\",\"pages\":\"789-800\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Belgian Mathematical Society-Simon Stevin\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.36045/j.bbms.200413\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Belgian Mathematical Society-Simon Stevin","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.36045/j.bbms.200413","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

给出了自反的严格凸的Gateaux光滑的Banach格$X$到Banach空间$Y$的正锥的$\varepsilon$ -等距$f$的弱稳定性界。该结果用于证明$\varepsilon$ -等距$f:(\mathbb{R}^n)^+\rightarrow Y$的稳定性定理，其中$\mathbb{R}^n$为具有$1$ -无条件范数的$n$维空间，$Y$为n维严格凸和Gateaux光滑空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Bulletin of the Belgian Mathematical Society-Simon Stevin 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Bulletin of the Belgian Mathematical Society - Simon Stevin (BBMS) is a peer-reviewed journal devoted to recent developments in all areas in pure and applied mathematics. It is published as one yearly volume, containing five issues. The main focus lies on high level original research papers. They should aim to a broader mathematical audience in the sense that a well-written introduction is attractive to mathematicians outside the circle of experts in the subject, bringing motivation, background information, history and philosophy. The content has to be substantial enough: short one-small-result papers will not be taken into account in general, unless there are some particular arguments motivating publication, like an original point of view, a new short proof of a famous result etc. The BBMS also publishes expository papers that bring the state of the art of a current mainstream topic in mathematics. Here it is even more important that at leat a substantial part of the paper is accessible to a broader audience of mathematicians. The BBMS publishes papers in English, Dutch, French and German. All papers should have an abstract in English.