Poisson transforms on right-angled Artin monoids

Abstract

We introduce the notion of the weak Brehmer's condition and prove that the Cauchy transform for a representation of a right-angled Artin monoid is bounded under such conditions. As a result, we obtain the Poisson transform and $\ast$-regular dilation for a family of operators that satisfies the weak Brehmer's condition and the property (P). This generalizes Popescu's notion of Cauchy and Poisson transforms for commuting families of row contractions.

arXiv comment16 pages