L^p([0,1])的均匀粗刚度

IF 0.7 3区数学 Q2 MATHEMATICS Studia Mathematica Pub Date : 2022-06-04 DOI:10.4064/sm220603-6-8

Christian Rosendal

{"title":"L^p([0,1])的均匀粗刚度","authors":"Christian Rosendal","doi":"10.4064/sm220603-6-8","DOIUrl":null,"url":null,"abstract":". If X is an almost transitive Banach space with amenable isometry group (for example, if X = L p ([0 , 1]) with 1 < p < ∞ ) and X admits a uniformly continuous map X φ −→ E into a Banach space E satisfying inf k x − y k = r (cid:13)(cid:13) φ ( x ) − φ ( y ) (cid:13)(cid:13) > 0 for some r > 0 (that is, φ is almost uncollapsed ), then X admits a simultaneously uniform and coarse embedding into a Banach space V that is ﬁnitely representable in L 2 ( E ).","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On uniform and coarse rigidity of $L^p([0,1])$\",\"authors\":\"Christian Rosendal\",\"doi\":\"10.4064/sm220603-6-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". If X is an almost transitive Banach space with amenable isometry group (for example, if X = L p ([0 , 1]) with 1 < p < ∞ ) and X admits a uniformly continuous map X φ −→ E into a Banach space E satisfying inf k x − y k = r (cid:13)(cid:13) φ ( x ) − φ ( y ) (cid:13)(cid:13) > 0 for some r > 0 (that is, φ is almost uncollapsed ), then X admits a simultaneously uniform and coarse embedding into a Banach space V that is ﬁnitely representable in L 2 ( E ).\",\"PeriodicalId\":51179,\"journal\":{\"name\":\"Studia Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-06-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studia Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/sm220603-6-8\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/sm220603-6-8","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: 1

摘要

．如果X是一个几乎传递巴拿赫空间与顺从的等距集团(例如,如果X = L p([0, 1])与1 < p <∞)和X承认均匀连续映射φ−→E为巴拿赫空间E满足正k X−y k = r (cid: 13) (cid: 13)φ(X)−φ(y) (cid: 13) (cid: 13) > 0对一些r > 0(φ几乎是气泡状),那么X承认同时制服和粗嵌入到巴拿赫空间V是在L有限表示的2 (E)。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

On uniform and coarse rigidity of $L^p([0,1])$

. If X is an almost transitive Banach space with amenable isometry group (for example, if X = L p ([0 , 1]) with 1 < p < ∞ ) and X admits a uniformly continuous map X φ −→ E into a Banach space E satisfying inf k x − y k = r (cid:13)(cid:13) φ ( x ) − φ ( y ) (cid:13)(cid:13) > 0 for some r > 0 (that is, φ is almost uncollapsed ), then X admits a simultaneously uniform and coarse embedding into a Banach space V that is ﬁnitely representable in L 2 ( E ).

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

Studia Mathematica 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

审稿时长

5 months

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.

期刊最新文献

A biparameter decomposition of Davis–Garsia type Embeddings between Lorentz sequence spaces are strictly but not finitely strictly singular Symmetric stable processes on amenable groups The $L^p$-to-$L^q$ compactness of commutators with $p \gt q$ $L^p$-boundedness of pseudo-differential operators on homogeneous trees