Abstract. The Sz.-Nagy--Foias model theory for $C_{\cdot0}$ contraction operators combined with the Beurling--Lax theorem establishes a correspondence between any two of four kinds of objects: shift-invariant subspaces, operator-valued inner functions, conservative discrete-time input/state/output linear systems, and $C_{\cdot0}$ Hilbert-space contraction operators. We discuss an analogue of all these ideas in the context of weighted Hardy spaces over the unit disk and an associated class of hypercontraction operators.

AMS Subject Classification (1991): 47A57

Keyword(s): Operator-valued functions, weighted Hardy space, Bergman inner functions, Beurling--Lax theorem, hypercontraction operators, dilation theory, characteristic function

Received December 7, 2012, and in final form May 19, 2013. (Registered under 109/2012.)