论文标题
在分解成对扭曲的收缩
On decomposition for pairs of twisted contractions
论文作者
论文摘要
本文介绍了Hilbert空间上各对扭曲收缩的Wold型分解。结果，我们获得了对双扭曲的异构体对的Wold型分解，尤其是Słoćinski定理的新的，简单的证明，用于对双重通勤异构的成对。我们还对成对的扭曲收缩进行了明确的分解，以便C.N.U.收缩部分为$ C_ {00} $。结果表明，对于以$ t $的收缩为$ t $的一对$（t，v^*）$，将$ v $作为等级计，在最小的等距扩张空间（$ t $）上存在一对唯一的（统一等效）的异常（统一等效）。作为一种应用，我们证明了由等轴测图和共同测量法组成的一对扭曲的操作员是双重扭曲的。最后，我们给出了一对双重扭曲的异构体的表征。
This paper presents Wold-type decomposition for various pairs of twisted contractions on Hilbert spaces. As a consequence, we obtain Wold-type decomposition for pairs of doubly twisted isometries and in particular, new and simple proof of Słoćinski's theorem for pairs of doubly commuting isometries are provided. We also achieve an explicit decomposition for pairs of twisted contractions such that the c.n.u. parts of the contractions are in $C_{00}$. It is shown that for a pair $(T,V^*)$ of twisted operators with $T$ as a contraction and $V$ as an isometry, there exists a unique (upto unitary equivalence) pair of doubly twisted isometries on the minimal isometric dilation space of $T$. As an application, we prove that pairs of twisted operators consisting of an isometry and a co-isometry are doubly twisted. Finally, we have given a characterization for pairs of doubly twisted isometries.
