Motivated by Ball, Li, Timotin and Trent's Schur-Agler class version of commutant lifting theorem, we introduce a class, denoted by ${\mathcal{P}}_n(\mathcal{H})$, of n-tuples of commuting contractions on a Hilbert space $\mathcal{H}$. We always assume that $n\ge 3$. The importance of this class of n-tuples stems from the fact that the von Neumann inequality or the existence of isometric dilation does not hold in general for n-tuples, $n\ge 3$, of commuting contractions on Hilbert spaces (even in the level of finite dimensional Hilbert spaces). Under some rank-finiteness assumptions, we prove that tuples in ${\mathcal{P}}_n(\mathcal{H})$ always admit explicit isometric dilations and satisfy a refined von Neumann inequality in terms of algebraic varieties in the closure of the unit polydisc in ${\mathbb{C}}^n$.

由Ball，Li，Timotin和Trent的Schur-Agler类版本的换向提升定理所激发，我们引入了一个类，表示为 ${\mathcal{P}}_{ñ}（\mathcal{H}）$，在希尔伯特空间上的n个元组的通勤收缩$\mathcal{H}$。我们总是假设$ñ\ge 3$。这类n元组的重要性源于von Neumann不等式或等距扩张的存在通常不适用于n元组，$ñ\ge 3$在希尔伯特空间（即使在有限维希尔伯特空间的水平上）的通缩收缩。在某些秩有限假设下，我们证明${\mathcal{P}}_{ñ}（\mathcal{H}）$ 在封闭单位圆盘时，总是允许明确的等距扩张并满足代数形式的精冯诺依曼不等式。 ${\mathbb{C}}^{ñ}$。