论文标题
$ \ Mathcal {u} _n $ twisted收缩的Wold-type分解
Wold-type decomposition for $\mathcal{U}_n$-twisted contractions
论文作者
论文摘要
令$ n> 1 $，和$ \ {u_ {ij} \} $，对于$ 1 \ leq i <j \ leq n $ be $ \ binom {n} {2} $ ponsiuting在希尔伯特space $ \ mathcal $ \ mathcal {h} $上的通勤litaries nimuties umintia $ \ Mathcal {h} $上的$ n $ - 收缩$（t_1，\ dots，t_n）$称为$ \ nathcal {u} _n $ twist twist twist twist twist $ \ \ \ \ \ {u_ {ij}} _ {ij} _ <j n $ <j {i <j} $ t_it_j = u_ {ij} t_jt_i; \ hspace {0.5cm} \ hspace {1cm} t_i^*t_j = u^*_ {ij} $ i，j，k = 1，\ dots，n $和$ i \ neq j $。 我们获得了一个配方，以计算$ \ Mathcal {u} _n $ twisted收缩的Hilbert Space上的Wold型分解的正交空间。作为副产品，已经建立了$ \ Mathcal {u} _2 $ -Twisted（或一对双重扭曲）和$ \ Mathcal {U} _n $ Twisted Isometries的新证明和完整结构。
Let $n>1$, and $\{U_{ij}\}$ for $1 \leq i < j \leq n$ be $\binom{n}{2}$ commuting unitaries on a Hilbert space $\mathcal{H}$ such that $U_{ji}:=U^*_{ij}$. An $n$-tuple of contractions $(T_1, \dots, T_n)$ on $\mathcal{H}$ is called $\mathcal{U}_n$-twisted contraction with respect to a twist $\{U_{ij}\}_{i<j}$ if $T_1, \dots, T_n$ satisfy \[ T_iT_j=U_{ij}T_jT_i; \hspace{0.5cm} \hspace{1cm} T_i^*T_j= U^*_{ij}T_jT_i^* \hspace{0.5cm} \mbox{and} \hspace{0.5cm} T_kU_{ij} =U_{ij}T_k \] for all $i,j,k=1, \dots, n$ and $i \neq j$. We obtain a recipe to calculate the orthogonal spaces of the Wold-type decomposition for $\mathcal{U}_n$-twisted contractions on Hilbert spaces. As a by-product, a new proof as well as complete structure for $\mathcal{U}_2$-twisted (or pair of doubly twisted) and $\mathcal{U}_n$-twisted isometries have been established.
