$c_0$的改造与最小位移问题

Annales Umcs, Mathematica Pub Date : 2014-12-01 DOI:10.1515/UMCSMATH-2015-0008

Łukasz Piasecki

{"title":"$c_0$的改造与最小位移问题","authors":"Łukasz Piasecki","doi":"10.1515/UMCSMATH-2015-0008","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to show that for every Banach space \$(X, \\|\\cdot\\|)\$ containing asymptotically isometric copy of the space \$c_0\$ there is a bounded, closed and convex set \$C \\subset X\$ with the Chebyshev radius \$r(C) = 1\$ such that for every \$k \\geq 1 \$ there exists a \$k\$-contractive mapping \$T : C \\to C\$ with \$\\| x - Tx \\| > 1 − 1/k\$ for any \$x \\in C\$.","PeriodicalId":340819,"journal":{"name":"Annales Umcs, Mathematica","volume":"7 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Renormings of $c_0$ and the minimal displacement problem\",\"authors\":\"Łukasz Piasecki\",\"doi\":\"10.1515/UMCSMATH-2015-0008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aim of this paper is to show that for every Banach space \\\$(X, \\\\|\\\\cdot\\\\|)\\\$ containing asymptotically isometric copy of the space \\\$c_0\\\$ there is a bounded, closed and convex set \\\$C \\\\subset X\\\$ with the Chebyshev radius \\\$r(C) = 1\\\$ such that for every \\\$k \\\\geq 1 \\\$ there exists a \\\$k\\\$-contractive mapping \\\$T : C \\\\to C\\\$ with \\\$\\\\| x - Tx \\\\| > 1 − 1/k\\\$ for any \\\$x \\\\in C\\\$.\",\"PeriodicalId\":340819,\"journal\":{\"name\":\"Annales Umcs, Mathematica\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Umcs, Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/UMCSMATH-2015-0008\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Umcs, Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/UMCSMATH-2015-0008","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

本文的目的是证明对于每一个巴拿赫空间 $(X, \|\cdot\|)$ 包含空间的渐近等距副本 $c_0$ 存在一个有界闭凸集 $C \subset X$ 切比雪夫半径 $r(C) = 1$ 这样对于每一个 $k \geq 1 $ 存在一个 $k$-收缩映射 $T : C \to C$ 有 $\| x - Tx \| > 1 − 1/k$ 对于任何 $x \in C$．

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

Renormings of $c_0$ and the minimal displacement problem

The aim of this paper is to show that for every Banach space $(X, \|\cdot\|)$ containing asymptotically isometric copy of the space $c_0$ there is a bounded, closed and convex set $C \subset X$ with the Chebyshev radius $r(C) = 1$ such that for every $k \geq 1 $ there exists a $k$-contractive mapping $T : C \to C$ with $\| x - Tx \| > 1 − 1/k$ for any $x \in C$.

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

Annales Umcs, Mathematica

自引率

0.00%

发文量