Operator theory on noncommutative varieties, II

An -tuple of operators on a Hilbert space is called a -constrained row contraction if and

where is a WOT-closed two-sided ideal of the noncommutative analytic Toeplitz algebra and is defined using the -functional calculus for row contractions.

We show that the constrained characteristic function associated with and is a complete unitary invariant for -constrained completely non-coisometric (c.n.c.) row contractions. We also provide a model for this class of row contractions in terms of the constrained characteristic functions. In particular, we obtain a model theory for -commuting c.n.c. row contractions.