Bulletin des Sciences Mathématiques ( IF 1.3 ) Pub Date : 2020-10-08 , DOI: 10.1016/j.bulsci.2020.102915 Sibaprasad Barik , B. Krishna Das , Jaydeb Sarkar
Motivated by Ball, Li, Timotin and Trent's Schur-Agler class version of commutant lifting theorem, we introduce a class, denoted by , of n-tuples of commuting contractions on a Hilbert space . We always assume that . 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, , 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 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 .
中文翻译:
等距扩张和冯·诺依曼不等式的有限秩通勤收缩
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 ,在希尔伯特空间上的n个元组的通勤收缩。我们总是假设。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,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 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。 。