论文标题
通过多项式特征函数通勤行收缩
Commuting row contractions with polynomial characteristic functions
论文作者
论文摘要
特征功能是在$ \ mathbb {c}^n $的开放单元球上定义的特殊操作员值分析功能，该函数与$ n $ tuple of $ n $ tuple consuting Row Crotation在某些Hilbert Space上。在本文中，我们继续研究具有多项式特征功能的希尔伯特空间上的$ n $ tumplass的表现。格里森的问题在行收缩的表示中起着重要作用。我们通过证明有关特征功能的因素化的定理，进一步补充了行收缩的表示。我们还强调了非交通运算符理论的重要性和作用，而非交通性品种对于多项式特征函数的分类问题。
A characteristic function is a special operator-valued analytic function defined on the open unit ball of $\mathbb{C}^n$ associated with an $n$-tuple of commuting row contraction on some Hilbert space. In this paper, we continue our study of the representations of $n$-tuples of commuting row contractions on Hilbert spaces, which have polynomial characteristic functions. Gleason's problem plays an important role in the representations of row contractions. We further complement the representations of our row contractions by proving theorems concerning factorizations of characteristic functions. We also emphasize the importance and the role of the noncommutative operator theory and noncommutative varieties to the classification problem of polynomial characteristic functions.
