Commutant Lifting Theorem in the Krein Space Setting: A Proof Based on theCoupling Method

摘要

A proof of the commutant lifting theorem for contractions of Krein spaces isgiven. This is done by adapting to the Krein space situation the Hilbert space proof based on the couplings of two contractions. Furthermore, a one to one correspondence between the contractive intertwining liftings and a family of isometric couplings is established.