{"title":"论成对扭曲收缩的分解","authors":"","doi":"10.1007/s11785-024-01497-2","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>This paper presents Wold-type decomposition for various pairs of twisted contractions on Hilbert spaces. We achieve an explicit decomposition for pairs of twisted contractions such that the c.n.u. parts of the contractions are in <span> <span>\\(C_{00}\\)</span> </span>. The structure for pairs of doubly twisted operators consisting of a power partial isometry has been discussed. It is also shown that for a pair <span> <span>\\((T,V^*)\\)</span> </span> of twisted operators with <em>T</em> as a contraction and <em>V</em> as an isometry, there exists a unique (up to unitary equivalence) pair of doubly twisted isometries on the minimal isometric dilation space of <em>T</em>. Finally, we have given a characterization for pairs of doubly twisted isometries. </p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"33 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Decomposition for Pairs of Twisted Contractions\",\"authors\":\"\",\"doi\":\"10.1007/s11785-024-01497-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3>Abstract</h3> <p>This paper presents Wold-type decomposition for various pairs of twisted contractions on Hilbert spaces. We achieve an explicit decomposition for pairs of twisted contractions such that the c.n.u. parts of the contractions are in <span> <span>\\\\(C_{00}\\\\)</span> </span>. The structure for pairs of doubly twisted operators consisting of a power partial isometry has been discussed. It is also shown that for a pair <span> <span>\\\\((T,V^*)\\\\)</span> </span> of twisted operators with <em>T</em> as a contraction and <em>V</em> as an isometry, there exists a unique (up to unitary equivalence) pair of doubly twisted isometries on the minimal isometric dilation space of <em>T</em>. Finally, we have given a characterization for pairs of doubly twisted isometries. </p>\",\"PeriodicalId\":50654,\"journal\":{\"name\":\"Complex Analysis and Operator Theory\",\"volume\":\"33 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-03-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complex Analysis and Operator Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11785-024-01497-2\",\"RegionNum\":4,\"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":"Complex Analysis and Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11785-024-01497-2","RegionNum":4,"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
摘要 本文提出了希尔伯特空间上各种成对扭曲收缩的沃尔德式分解。我们实现了对扭曲收缩的明确分解，使得收缩的c.n.u.部分在\(C_{00}\)中。我们讨论了由幂部分等距构成的成对双扭转算子的结构。我们还证明，对于一对以 T 为收缩、V 为等势的扭曲算子对 \((T,V^*)\)，在 T 的最小等距扩张空间上存在一对唯一的（直到单元等价）双扭曲等势。
On Decomposition for Pairs of Twisted Contractions
Abstract
This paper presents Wold-type decomposition for various pairs of twisted contractions on Hilbert spaces. We achieve an explicit decomposition for pairs of twisted contractions such that the c.n.u. parts of the contractions are in \(C_{00}\). The structure for pairs of doubly twisted operators consisting of a power partial isometry has been discussed. It is also shown that for a pair \((T,V^*)\) of twisted operators with T as a contraction and V as an isometry, there exists a unique (up to unitary equivalence) pair of doubly twisted isometries on the minimal isometric dilation space of T. Finally, we have given a characterization for pairs of doubly twisted isometries.
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