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arXiv · 1709.08152

An essential representation for a product system over a finitely generated subsemigroup of $\mathbb{Z}^{d}$

S. P. Murugan·S. Sundar
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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 $\alpha$.

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S. P. Murugan, S. Sundar. 2017-09-24. An essential representation for a product system over a finitely generated subsemigroup of $\mathbb{Z}^{d}$. https://arxiv.org/abs/1709.08152

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