2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126021We develop a dilation theory for row contractions subject to constraints determined by sets of noncommutative polynomials. Under natural conditions on the constraints, we have uniqueness for the minimal dilation. A characteristic function is associated with any (constrained) row contraction. For pure constrained row contraction, we show that the characteristic function is a complete unitary invariant and provide a model. We also show that the curvature invariant and Euler characteristic asssociated with a Hilbert module generated by an arbitrary (resp. commuting) row contraction can be expressed only in terms of the corresponding (resp. constrained) characteristic function. We provide a commutant lifting theorem for pure constrained row contractions and obtain a Nevanlinna-Pick interpolation result in this setting. Our theory includes, in particular, the commutative and q-commutative cases, while the standard noncommutative dilation theory for row contractions serves as a "universal model".CommentsOperator AlgebrasFunctional Analysis47A20, 47A56, 47A13, 47A63text