与非交换变量相关的C * -代数表示的世界分解

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Operator Theory Pub Date : 2021-12-15 DOI:10.7900/jot.2020jun29.2289

Gelu Popescu

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引用次数: 3

摘要

给定非对易不确定性Z1，…，Zn中的一组多项式Q和一个正则域Dmp（H）⊂B（H）n，m，n∈n，与一个正正则多项式p∈C⟨Z1，..，Zn⟩相关联，我们考虑所有g∈Q}的变量VQ（H）：＝{X=（X1，…，Xn）∈Dmp（H）：g（X）=0。每个变种VQ（H）都允许一个｛\ it通用模型｝B＝（B1，…，Bn）。本文的主要目的是研究由B1，…，Bn和恒等式生成的C*-代数C*（VQ）的*-表示的结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Wold decompositions for representations of C∗-algebras associated with noncommutative varieties

Given a set Q of polynomials in noncommutative indeterminates Z1,…,Zn and a regular domain Dmp(H)⊂B(H)n, m,n∈N, associated with a positive regular polynomial p∈C⟨Z1,…,Zn⟩, we consider the variety VQ(H):={X=(X1,…,Xn)∈Dmp(H):g(X)=0 for all g∈Q}. Each variety VQ(H) admits a {\it universal model} B=(B1,…,Bn). The main goal of the paper is to study the structure of the ∗-representations of the C∗-algebra C∗(VQ) generated by B1,…,Bn and the identity.

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来源期刊

Journal of Operator Theory 数学-数学

CiteScore

1.30

自引率

12.50%

发文量

审稿时长

12 months

期刊介绍： The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.