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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214047Let E be a product system of C*-correspondences over N^r. 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.20 pages; the final version will appear in the Indiana University Mathematics Journal (v2 contains a few minor corrections suggested by Orr Shalit)Operator AlgebrasFunctional Analysis47A20 (Primary) 05C20, 46L08, 47A13 (Secondary)On isometric dilations of product systems of C*-correspondences and applications to families of contractions associated to higher-rank graphstext