The Arveson Extension Theorem and coanalytic models

We develop techniques which allow one to describe in simple terms the set of operators on Hilbert space of the form M^{* ()} |M, where M is multiplication by z on a Hilbert space of analytic functions satisfying certain technical assumptions, M^{* ()} is the direct sum of a countably infinite number of copies of M^*, andM is invariant for M^{* ()}. One of the main ingredients in our technique is the Arveson Extension Theorem and this paper illustrates the great power and tractability of that theorem in a concrete setting.Research partially supported by NSF grant MCS 81-02518