Isometric Dilations of Representations of Product Systems via Commutants
arXiv:math/0602459
Abstract
We construct a weak dilation of a not necessarily unital CP-semigroup to an E-semigroup acting on the adjointable operators of a Hilbert module with a unit vector. We construct the dilation in such a way that the dilating E-semigroup has a pre-assigned product system. Then, making use of the commutant of von Neumann correspondences, we apply the dilation theorem to proof that covariant representations of product systems admit isometric dilations.
Switched some definitions directly after theorems in Sect. 1, included (>6 pp.) introduction to von Neumann correspondences (Sect. 3). To appear in International Journal of Mathematics