乘积系统表示的正则展开式

Mathematical Proceedings of the Royal Irish Academy Pub Date : 2005-04-07 DOI:10.3318/PRIA.2008.108.1.89

B. Solel

{"title":"乘积系统表示的正则展开式","authors":"B. Solel","doi":"10.3318/PRIA.2008.108.1.89","DOIUrl":null,"url":null,"abstract":"We study completely contractive representations of product systems $X$ of correspondences over the semigroup $\\mathbb{Z}_+^k$. We present a necessary and sufficient condition for such a representation to have a regular isometric dilation. We discuss representations that doubly commute and show that these representations induce completely contractive representations of the norm closed algebra generated by the image of the Fock representation of $X$.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"55 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"36","resultStr":"{\"title\":\"REGULAR DILATIONS OF REPRESENTATIONS OF PRODUCT SYSTEMS\",\"authors\":\"B. Solel\",\"doi\":\"10.3318/PRIA.2008.108.1.89\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study completely contractive representations of product systems $X$ of correspondences over the semigroup $\\\\mathbb{Z}_+^k$. We present a necessary and sufficient condition for such a representation to have a regular isometric dilation. We discuss representations that doubly commute and show that these representations induce completely contractive representations of the norm closed algebra generated by the image of the Fock representation of $X$.\",\"PeriodicalId\":434988,\"journal\":{\"name\":\"Mathematical Proceedings of the Royal Irish Academy\",\"volume\":\"55 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-04-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"36\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Proceedings of the Royal Irish Academy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3318/PRIA.2008.108.1.89\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Royal Irish Academy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3318/PRIA.2008.108.1.89","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 36

摘要

我们研究了半群$\mathbb{Z}_+^k$上对应的乘积系统$X$的完全压缩表示。我们给出了这种表示具有正则等距膨胀的充分必要条件。我们讨论了双交换的表示，并证明了这些表示诱导出由$X$的Fock表示的象生成的范数闭代数的完全压缩表示。

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

REGULAR DILATIONS OF REPRESENTATIONS OF PRODUCT SYSTEMS

We study completely contractive representations of product systems $X$ of correspondences over the semigroup $\mathbb{Z}_+^k$. We present a necessary and sufficient condition for such a representation to have a regular isometric dilation. We discuss representations that doubly commute and show that these representations induce completely contractive representations of the norm closed algebra generated by the image of the Fock representation of $X$.

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

Mathematical Proceedings of the Royal Irish Academy

自引率

0.00%

发文量