等距膨胀与多变量中的Sarason交换子提升定理
Isometric dilation and Sarason's commutant lifting theorem in several variables
AI总结：
本文针对n≥3的可交换压缩算子元组，构造BCL型等距膨胀，证明von Neumann不等式及Sarason型交换子提升定理，并发现新的可膨胀算子类。
摘要：
本文研究一类由n个（n≥3）可交换压缩算子构成的n元组的等距膨胀与交换子提升问题。我们证明该类中的算子元组可膨胀为BCL型的可交换等距算子元组。作为这种显式膨胀的结果，我们证明其von Neumann不等式在闭单位多圆盘的一维子簇上成立。基于此膨胀，我们通过证明每个交换子都能以可交换且保范的方式提升到膨胀空间，从而证明了Sarason型的交换子提升定理。这进一步引导我们找到另一类由n个（n≥3）可交换压缩算子构成的n元组，其中每个元组均具有等距膨胀。
英文摘要：
The article deals with isometric dilation and commutant lifting for a class of $n$-tuples $(n \geq 3)$ of commuting contractions. We show that operator tuples in the class dilate to tuples of commuting isometries of BCL type. As a consequence of such an explicit dilation, we show that their von Neumann inequality holds on a one dimensional variety of the closed unit polydisc. On the basis of such a dilation, we prove a commutant lifting theorem of Sarason's type by establishing that every commutant can be lifted to the dilation space in a commuting and norm preserving manner. This further leads us to find yet another class of $n$-tuples $(n\geq 3)$ of commuting contractions each of which possesses isometric dilation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
