{"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}
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 $X$.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
