An essential representation for a product system over a finitely generated subsemigroup of ℤ^d

2017/09/24 by Murugan, S. P., Sundar, S.
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1709.08152

Abstract

Let S ⊂ ℤ^d be a finitely generated subsemigroup. Let E be a product system over S. We show that there exists an infinite dimensional separable Hilbert space H and a semigroup α:=\α_x\_{x ∈ S} of unital normal *-endomorphisms of B(H) such that E is isomorphic to the product system associated to α.

Related

• On the existence of E₀-semigroups
• E₀^P-semigroups and product systems
• Is Every Product System Concrete?
• Representations of product systems over semigroups and dilations of commuting CP maps
• *-semigroup endomorphisms of B(H)