Representing a product system representation as a contractive semigroup and applications to regular isometric dilations

Orr Moshe Shalit

doi:10.4153/CMB-2010-060-8

Representing a product system representation as a contractive semigroup and applications to regular isometric dilations

Orr Moshe Shalit

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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 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 ℝ ₊ ^k.

Original language	English
Pages (from-to)	550-563
Number of pages	14
Journal	Canadian Mathematical Bulletin
Volume	53
Issue number	3
DOIs	https://doi.org/10.4153/CMB-2010-060-8
State	Published - 1 Sep 2010
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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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 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 ℝ + k.",

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AB - 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 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 ℝ + k.

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M3 - Article

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EP - 563

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

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Representing a product system representation as a contractive semigroup and applications to regular isometric dilations

Abstract

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