IUMJ

Title: On isometric dilations of product systems of $C*$-correspondences and applications to families of contractions associated to higher-rank graphs

Authors: Adam Skalski

Issue: Volume 58 (2009), Issue 5, 2227-2252

Abstract:

Let $\mathbb{E}$ be a product system of $C^{*}$-correspondences over $\mathbb{N}_0^r$. Some sufficient conditions for the existence of a not necessarily regular isometric dilation of a completely contractive representation of $\mathbb{E}$ are established and difference between regular and $^{*}$-regular dilations discussed. It is in particular shown that a minimal isometric dilation is $^{*}$-regular if and only if it is doubly commuting. The case of product systems associated with higher-rank graphs is analysed in detail.