Representing a Product System Representation as a Contractive Semigroup and Applications to Regular Isometric Dilations

http://dx.doi.org/10.4153/CMB-2010-060-8
Canad. Math. Bull. 53(2010), 550-563

  Published:2010-06-11
 Printed: Sep 2010

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 $\mathbb{N}^k$ 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 $\mathbb R_{+}^k$.