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

Open Access article
 Printed: Sep 2010
  • Orr Moshe Shalit,
    Department of Mathematics, Technion, Haifa, Israel
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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 $\mathbb R_{+}^k$.
MSC Classifications: 47A20, 46L08 show english descriptions Dilations, extensions, compressions
47A20 - Dilations, extensions, compressions
46L08 - $C^*$-modules

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