Regular Dilation on Graph Products of $\mathbb{N}$

Boyu Li

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arXiv · 1612.02733

Regular Dilation on Graph Products of $\mathbb{N}$

Boyu Li

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Abstract

We extended the definition of regular dilation to graph products of $\mathbb{N}$, which is an important class of quasi-lattice ordered semigroups. Two important results in dilation theory are unified under our result: namely, Brehmer's regular dilation on $\mathbb{N}^k$ and Frazho-Bunce-Popescu's dilation of row contractions. We further show that a representation of a graph product has an isometric Nica-covariant dilation if and only if it is $\ast$-regular. A special case of our result was considered by Popescu, and we studied the connection with Popescu's work.

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Boyu Li. 2016-12-08. Regular Dilation on Graph Products of $\mathbb{N}$. https://arxiv.org/abs/1612.02733

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