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

Abstract

Let E be a product system of C*-correspondences over ℕ r 0 . Some sufficient conditions for the existence of a not necessarily regular isometric dilation of a completely contractive representation of 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.