Θₙ上纯Θₙ-压缩算子的膨胀与函数模型及特征簇上的冯·诺依曼不等式
Dilation and Functional Models for Pure $\mathbfΘ_n$-Contractions and the von Neumann Inequality on Distinguished Varieties in $\mathbfΘ_n$
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中文总结 AI 辅助
本文引入Θₙ中特征簇概念，证明其行列式表示与多项式凸性，得到纯Θₙ-压缩算子的膨胀与函数模型，还证明特定Θₙ-压缩算子下对应代数簇上成立冯·诺依曼不等式。
中文摘要 AI 辅助
本文引入了区域Θₙ中特征簇的概念，主要结果之一是给出了Θₙ中每个特征簇的行列式表示；还证明了每个特征簇的闭包是多项式凸的。此外，我们得到了一类纯Θₙ-压缩算子的膨胀与函数模型。最后，对于Θₙ-压缩算子T=(T₁,…,Tₙ)，若Tₙ^*是纯压缩算子，则存在Θₙ中的代数簇，使得该簇的闭包与Θₙ的特征边界的交集上成立冯·诺依曼不等式。
英文摘要
In this paper, we introduce the notion of a distinguished variety in the domain $\mathbfΘ_n$. One of the main results of the paper is a determinantal representation for every distinguished variety in $\mathbfΘ_n$. We also show that the closure of every distinguished variety is polynomially convex. Furthermore, we obtain a dilation and a functional model for a class of pure $\mathbfΘ_n$-contractions. Finally, we show that for a $\mathbfΘ_n$-contraction $\mathbf{T}=(T_1,\dots,T_n)$ such that $T_n^*$ is a pure contraction, there exists an algebraic variety in $\mathbfΘ_n$ for which the von Neumann inequality holds on the intersection of the closure of the variety with the distinguished boundary of $\mathbfΘ_n$.
