论文标题
扭曲功率部分异构体的结构
The structure of twisted power partial isometries
论文作者
论文摘要
令$ n> 1 $，然后让$ \ {u_ {ij} \} _ {1 \ leq i <j \ leq n} $ be $ n \ be $ n \ select 2 $ commuting Unting Unting Unting Unting Unitaries在Hilbert Space $ \ Mathcal {H} $上。假设$ u_ {ji}：= u^*_ {ij} $，$ 1 \ leq i <j \ leq n $。 Hilbert Space上的Power Power a部分等法$（V_1，...，...，V_N）$ $ \ MATHCAL {H} $称为$ \ MATHCAL {U} _n $ twisted Power power power power power power power power power power power power power power power power power power power power power power power power power power power power power power power power power power power atial sol如果$ \ {u_ {u_ {ij} \} _ {ij} _ {i <j} $从上下文中可以清楚地清楚$ \ {u_ {u_ {ij} _ {ij} _ { ~~ \ text {和} ~~ v_ku_ {ij} = u_ {ij} v_k ~~（i，j，j，k = 1,2，... \ cite {HW70}键入正交分解。
Let $n>1$ and let $\{U_{ij}\}_{1\leq i<j\leq n}$ be $n\choose 2$ commuting unitaries on a Hilbert space $\mathcal{H}$. Suppose $U_{ji}:=U^*_{ij}$, $1\leq i<j\leq n$. An n-tuple of power partial isometries $(V_1,...,V_n)$ on Hilbert space $\mathcal{H}$ is called $\mathcal{U}_n$-twisted power partial isometry with respect to $\{U_{ij}\}_{i<j}$ (or simply $\mathcal{U}_n$-twisted power partial isometry if $\{U_{ij}\}_{i<j}$ is clear from the context) if $V_i^*V_j=U_{ij}V_jV^*_i, ~~ V_iV_j=U_{ji}V_jV_i ~~\text{and}~~ V_kU_{ij}=U_{ij}V_k~~(i,j,k=1,2,...,n,~\text{and}~i\neq j).$ We prove that each $\mathcal{U}_n$-twisted power partial isometry admits a Halmos and Wallen \cite{HW70} type orthogonal decomposition.
