On the existence of E0-semigroups — the multiparameter case

Abstract

Let [Formula: see text] be a closed convex cone. Assume that [Formula: see text] is pointed, i.e. the intersection [Formula: see text] and [Formula: see text] is spanning, i.e. [Formula: see text]. Denote the interior of [Formula: see text] by [Formula: see text]. Let [Formula: see text] be a product system over [Formula: see text]. We show that there exists an infinite-dimensional separable Hilbert space [Formula: see text] and a semigroup [Formula: see text] of unital normal ∗-endomorphisms of [Formula: see text] such that [Formula: see text] is isomorphic to the product system associated to [Formula: see text].