Regular dilations of representations of product systems

Abstract

We study completely contractive representations of product systems $X$ of correspondences over the semigroup ${\mathbb{Z}}_{+}^k$. We present a necessary and sufficient condition for such a representation to have a regular isometric dilation. We discuss representations that doubly commute and show that these representations induce completely contractive representations of the norm closed algebra generated by the image of the Fock representation of $X$.

30 pages, Latex

References in corpus (1)

• Representations of product systems over semigroups and dilations of commuting CP maps