Sz.-Nagy and Foias proved that each $C_{ \cdot0}$-contraction has a dilation to a Hardy shift and thus established an elegant analytic functional model for contractions of class $C_{ \cdot0}$. This has motivated lots of further works on model theory and generalizations to commuting tuples of $C_{ \cdot0}$-contractions. In this paper, we focus on doubly commuting sequences of $C_{ \cdot0}$-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.
Categories: math.FA