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

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

Murugan, S P; Sundar, S

Proceedings of the Indian Academy of Sciences. Mathematical sciences, 01/2019, Volume: 129, Issue: 2

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Let S⊂Zd 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:={αx}x∈S of unital normal ∗-endomorphisms of B(H) such that E is isomorphic to the product system associated to α.

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