Isometric dilations for representations of product systems
Isometric dilations for representations of product systems
We discuss representations of product systems (of $W^*$ -correspondences) over the semigroup $\mathbb{Z}^n_+$ and show that, under certain pureness and Szegö positivity conditions, a completely contractive representation can be dilated to an isometric representation. For $n=1,2$ this is known to hold in general (without assuming the conditions), but for $n\geq …