“…We follow the approach adopted in [17]: first we present a version of the Arov-Grossman model which provides a parameterization of the minimal unitary Hilbert space extensions of a given Kreȋn space isometry whose defect subspaces are Hilbert spaces, then we use it to parameterize the minimal weak unitary Hilbert space dilations of a given continuous bicontraction X defined on a regular subspace B of a Kreȋn space H such that H B is a Hilbert subspace of H, finally we tackle the relaxed commutant lifting problem with a given data set {C, T , V T , R, Q} of five Kreȋn space operators, where T is a continuous bicontraction, and give a parametric descriptions of the interpolants in this setting. In addressing the lifting problem we apply the coupling method to get a continuous bicontraction X from the data set {C, T , V T , R, Q} and we show that the interpolants can be obtained from a subclass of the minimal weak unitary Hilbert space dilations of X.…”