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An essential representation for a product system over a finitely generated subsemigroup of \(\pmb {{\mathbb {Z}}}^{{\varvec{d}}}\)

  • S P Murugan
  • S SundarEmail author
Article

Abstract

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

Keywords

\(E_0^{P}\)-semigroups essential representations product systems 

Mathematics Subject Classification

Primary: 46L55 Secondary: 46L99 

Notes

Acknowledgements

The authors would like to thank Prof. Partha Sarathi Chakraborty for his geometric insight which helped them in proving Lemma 3.8.

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Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Chennai Mathematical InstituteChennaiIndia

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