Dilation theory and analytic model theory for doubly commuting sequences of C._(0)-contractions  

作　　者：Hui Dan Kunyu Guo 

机构地区：[1]College of Mathematics,Sichuan University,Chengdu 610065,China [2]School of Mathematical Sciences,Fudan University,Shanghai 200433,China

出　　处：《Science China Mathematics》2023年第2期303-340,共38页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11871157 and 12101428)。

摘　　要：It is known that every C·_(0)-contraction has a dilation to a Hardy shift.This leads to an elegant analytic functional model for C·_(0)-contractions,and has motivated lots of further works on the model theory and generalizations to commuting tuples of C·_(0)-contractions.In this paper,we focus on doubly commuting sequences of C·_(0)-contractions,and establish the dilation theory and the analytic model theory for these sequences of operators.These results are applied to generalize the Beurling-Lax theorem and Jordan blocks in the multivariable operator theory to the operator theory in the infinite-variable setting.

关 键 词：doubly commuting sequence dilation theory analytic functional model Beurling-Lax theorem Jordan block 

分 类 号：O17[理学—数学]