BOUNDED CHARACTERISTIC FUNCTIONS AND MODELS FOR NONCONTRACTIVE SEQUENCES OF OPERATORS

The Sz.-Nagy-Foias functional model for completely non-unitary contractions is extended to completely non-coisometric sequences of bounded operators T = (T1,... ,Td) (d finite or infinite) on a Hilbert space, with bounded characteristic functions. For this class of sequences, it is shown that the characteristic function (theta)- is a complete unitary invariant. We obtain, as the main result, necessary and sufficient conditions for a bounded multi-analytic operator on Fock spaces to coincide with the characteristic function associated with a completely non-coisometric sequence of bounded operators on a Hilbert space.