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Representing a Product System Representation as a Contractive Semigroup and Applications to Regular Isometric Dilations
Published online by Cambridge University Press: 20 November 2018
Abstract
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
$\mathbb{R}_{+}^{k}$.
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- Copyright © Canadian Mathematical Society 2010
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