Representing a product system representation as a contractive semigroup and applications to regular isometric dilations
نویسنده
چکیده
In this paper we propose a new technical tool for analyzing representations of Hilbert C∗-product systems. Using this tool, we give a new proof that every doubly commuting representation over N has a regular isometric dilation, and we also prove sufficient conditions for the existence of a regular isometric dilation of representations over more general subsemigroups of Rk+.
منابع مشابه
On Isometric Dilations of Product Systems of C-correspondences and Applications to Families of Contractions Associated to Higher-rank Graphs
Let E be a product system of C-correspondences over Nr 0 . Some sufficient conditions for the existence of a not necessarily regular isometric dilation of a completely contractive representation of E are established and difference between regular and -regular dilations discussed. It is in particular shown that a minimal isometric dilation is -regular if and only if it is doubly commuting. The c...
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تاریخ انتشار 2008