论文标题
分解Toeplitz操作员
Factorization of Toeplitz operators
论文作者
论文摘要
在本文中，通过考虑$ t =（t_1，\ dots，t_d）$，$ d $ - 在希尔伯特太空$ \ mathcal {h} $上的通勤收缩，我们研究$ t $ t $ -to-to-to-to-to-to-to-to-toeplitz运营商，这些操作员由$ \ nathcal com y Mathcal的$ \ mathcal { $ i = 1，\ dots，d $。我们表明，任何正面的$ t $ to-to-toeeplitz运算符都可以根据$ t $的等距伪扩张来分解。对于正纯$ t $ toeplitz运营商，还获得了类似的分解结果。但是，后一种分解是根据$ t $的特殊类型的等距伪扩展而获得的，并且在案例$ d = 2 $和$ d> 2 $之间观察到了一定的差异。在更一般的环境中，通过考虑$ d $ tumplass的通勤收缩$ s $和$ t $，我们还研究了$（s，t）$ - toeplitz运营商。
In this article, by considering $T=(T_1,\dots, T_d)$, an $d$-tuple of commuting contractions on a Hilbert space $\mathcal{H}$, we study $T$-Toeplitz operators which consists of bounded operators $X$ on $\mathcal{H}$ such that \[ T_i^*XT_i=X \] for all $i=1,\dots,d$. We show that any positive $T$-Toeplitz operator can be factorized in terms of an isometric pseudo-extension of $T$. A similar factorization result is also obtained for positive pure lower $T$-Toeplitz operators. However, the latter factorization is obtained in terms of a special type of isometric pseudo-extension of $T$, and a certain difference has been observed between the case $d=2$ and $d>2$. In a more general context, by considering $d$-tuples of commuting contractions $S$ and $T$, we also study $(S, T)$-Toeplitz operators.
