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

Orr Shalit

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arXiv · 0706.3178

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

Orr Shalit

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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 $\mathbb{N}^k$ 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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Orr Shalit. 2007-06-21. Representing a product system representation as a contractive semigroup and applications to regular isometric dilations. https://arxiv.org/abs/0706.3178

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