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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

Orr Moshe Shalit
Orr Moshe Shalit*
Affiliation:
Department of Mathematics, Technion, Haifa, Israel e-mail: orrms@tx.technion.ac.il
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Abstract

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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 $\mathbb{R}_{+}^{k}$.

Keywords

47A2046L08
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 3 , 01 September 2010 , pp. 550 - 563
Copyright
Copyright © Canadian Mathematical Society 2010

References

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