关于超循环算子集

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-05-07 DOI:10.1112/blms.13067

Thiago R. Alves, Gustavo C. Souza

{"title":"关于超循环算子集","authors":"Thiago R. Alves, Gustavo C. Souza","doi":"10.1112/blms.13067","DOIUrl":null,"url":null,"abstract":"In this article, we address a problem posed by Bayart regarding the existence of an infinite-dimensional closed vector subspace (excluding the null operator) within the set of supercyclic operators on Banach spaces. We fully resolve this problem by establishing the existence of the closed subspace. Furthermore, we prove that the set of supercyclic operators on <math>\n <semantics>\n <msub>\n <mi>ℓ</mi>\n <mn>1</mn>\n </msub>\n <annotation>$\\ell _1$</annotation>\n </semantics></math> contains, up to the null operator, an isometric copy of <math>\n <semantics>\n <msub>\n <mi>ℓ</mi>\n <mn>1</mn>\n </msub>\n <annotation>$\\ell _1$</annotation>\n </semantics></math>.","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 7","pages":"2483-2494"},"PeriodicalIF":0.8000,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the set of supercyclic operators\",\"authors\":\"Thiago R. Alves, Gustavo C. Souza\",\"doi\":\"10.1112/blms.13067\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we address a problem posed by Bayart regarding the existence of an infinite-dimensional closed vector subspace (excluding the null operator) within the set of supercyclic operators on Banach spaces. We fully resolve this problem by establishing the existence of the closed subspace. Furthermore, we prove that the set of supercyclic operators on <math>\\n <semantics>\\n <msub>\\n <mi>ℓ</mi>\\n <mn>1</mn>\\n </msub>\\n <annotation>$\\\\ell _1$</annotation>\\n </semantics></math> contains, up to the null operator, an isometric copy of <math>\\n <semantics>\\n <msub>\\n <mi>ℓ</mi>\\n <mn>1</mn>\\n </msub>\\n <annotation>$\\\\ell _1$</annotation>\\n </semantics></math>.\",\"PeriodicalId\":55298,\"journal\":{\"name\":\"Bulletin of the London Mathematical Society\",\"volume\":\"56 7\",\"pages\":\"2483-2494\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the London Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/blms.13067\",\"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":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.13067","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

摘要

在这篇文章中，我们讨论了巴亚特提出的一个问题，即在巴拿赫空间上的超循环算子集合中是否存在一个无限维的封闭向量子空间（不包括空算子）。我们通过确定封闭子空间的存在，完全解决了这个问题。此外，我们还证明了 ℓ 1 $\ell _1$ 上的超循环算子集合包含了空算子，即 ℓ 1 $\ell _1$ 的等距副本。

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 the set of supercyclic operators

In this article, we address a problem posed by Bayart regarding the existence of an infinite-dimensional closed vector subspace (excluding the null operator) within the set of supercyclic operators on Banach spaces. We fully resolve this problem by establishing the existence of the closed subspace. Furthermore, we prove that the set of supercyclic operators on $ℓ_{1}$ contains, up to the null operator, an isometric copy of $ℓ_{1}$ .