# Dilation theory and analytic model theory for doubly commuting sequences of $C_{.0}$-contractions

## TL;DR

This paper develops dilation and analytic model theories for doubly commuting sequences of $C_{0}$-contractions, extending classical results to infinite-variable operator settings and generalizing key theorems like Beurling-Lax.

## Contribution

It introduces dilation and model theories for doubly commuting sequences of $C_{0}$-contractions, expanding multivariable operator theory to infinitely many variables.

## Key findings

- Established dilation theory for doubly commuting $C_{0}$-contraction sequences.
- Developed an analytic model theory for these sequences.
- Generalized Beurling-Lax theorem and Jordan blocks to infinite variables.

## Abstract

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.