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

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

2008-09-25

arxiv.org/abs/0809.4348v2

Mathematics

Operator Algebras

20 pages; the final version will appear in the Indiana University Mathematics Journal (v2 contains a few minor corrections sug

Scientific paper

Let 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.

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