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arXiv · 0809.4348

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

Adam Skalski
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Abstract

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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Adam Skalski. 2009-01-05. On isometric dilations of product systems of C*-correspondences and applications to families of contractions associated to higher-rank graphs. https://arxiv.org/abs/0809.4348

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