Analysis Seminar

Boyu Li, Department of Pure Mathematics, University of Waterloo

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

We extend the definition of a 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 the 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 *-regular. This is related to Popescu's property (P) when the underlying graph is a complete multipartite graph.

MC 5417