2019/07/12 by Dan, Hui, Guo, Kunyu
#46E50 #47A13 #47A20 #47A45 #47B32 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1907.05815
Sz.-Nagy and Foias proved that each C⋅0-contraction has a dilation to a Hardy shift and thus established an elegant analytic functional model for contractions of class C⋅0. This has motivated lots of further works on 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 countably infinitely many variables.