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

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

2007-06-21

arxiv.org/abs/0706.3178v1

Canadian Mathematical Bulletin, Vol. 53, No. 3 (2010) 550-563

Mathematics

Operator Algebras

15 pages

Scientific paper

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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