论文标题
常规$λ$ - polyballs上的功能性演算和多分析模型
Functional calculus and multi-analytic models on regular $Λ$-polyballs
论文作者
论文摘要
本文的目的是介绍和研究与常规$λ$ - polyball相关的非交通性耐寒空间，以在完全非涂层的非共同耐硬度空间上开发功能性演算（c.n.c.）$ k $ - $ k $ -tuplys $ {\ bf bf b}_λ（h）$和功能cormantions和coptions c。常规$λ$ - polyball中的元素。此外，我们表明特征函数是C.N.C类的完全统一不变。 $ k $ -tuples中的$ {\ bf b}_λ（h）$。这些结果扩展了sz.-nagy-foia \ c s的相应经典结果，用于收缩和行收缩的非交换版本。在特定情况下，当$ n_1 = \ cdots = n_k = 1 $和$λ_{ij} = 1 $时，我们就可以根据$ k $的特征功能获得功能性计算和操作员模型理论 - 满足Brehmer条件的收缩。
The goal of the present paper is to introduce and study noncommutative Hardy spaces associated with the regular $Λ$-polyball, to develop a functional calculus on noncommutative Hardy spaces for the completely non-coisometric (c.n.c.) $k$-tuples in ${\bf B}_Λ(H)$, and to study the characteristic functions and the associated multi-analytic models for the c.n.c. elements in the regular $Λ$-polyball. In addition, we show that the characteristic function is a complete unitary invariant for the class of c.n.c. $k$-tuples in ${\bf B}_Λ(H)$. These results extend the corresponding classical results of Sz.-Nagy--Foia\c s for contractions and the noncommutative versions for row contractions. In the particular case when $n_1=\cdots=n_k=1$ and $Λ_{ij}=1$, we obtain a functional calculus and operator model theory in terms of characteristic functions for $k$-tuples of contractions satisfying Brehmer condition.
