Year: 2016
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Li, Boyu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2590184580