On Commutant Lifting with Finite Defect, II

In the lifting theorem of B. Sz.-Nagy, C. Foiaş, and D. Sarason the intertwining operatorA, the operator that is lifted, is a contraction from one Hilbert space to another. J. A. Ball and J. W. Helton showed that a kind of lifting theorem still holds if the negative spectral subspace of the operatorI−A*Ais finite dimensional. In this paper we prove that this result remains valid if the Hilbert spaces are replaced by spaces with an indefinite metric.