A Schur type analysis of the minimal weak unitary Hilbert space dilations of a Kreĭn space bicontraction and the Relaxed Commutant Lifting Theorem in a Kreĭn space setting

A parameterization of the minimal weak unitary Hilbert space dilations of a given continuous bicontractive operator on a Kreĭn space by means of operator-valued Schur functions is obtained from the Arov–Grossman functional model. The result is combined with the coupling method to give a parametric description of the interpolants in a Kreĭn space version of the Relaxed Commutant Lifting Theorem.