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

Proceedings of the Indian Academy of Sciences. Mathematical sciences

S P MURUGAN^1¹ 

[1] Chennai Mathematical Institute, Siruseri, Chennai 603 103, India^1

关键词: $E^{P}_{0}$ -semigroups;    essential representations;    product systems;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 $\ast$-endomorphisms of $B(\mathcal{H})$ such that $E$ is isomorphic to the product system associated to $\alpha$.

【 授权许可】

CC BY