Factorization of Characteristic Functions of Iterated Liftings

We obtain a factorization of the characteristic function of a contractive two-step iterated lifting in terms of the characteristic functions of constituent liftings of the iterated lifting and the Julia-Halmos matrix. We also give an expression for the characteristic function of the minimal part of a contractive two-step iterated lifting as a restriction of the product of the characteristic functions of constituent liftings of the iterated lifting.