Commutant Lifting Theorem for Contractions on Krein Spaces

摘要

A proof of the commutant lifting theorem for contractions on Krein spaces is given. This is done by associating to the data a suitable isometry V so that a solution of the lifting problem is obtained directly from a unitary Hilbert space extension of V. Furthermore, a bijective correspondence between the solutions and the family of all minimal unitary Hilbert space extensions of V is established. In the Hilbert space case, the method is due to R. Arocena.