A FACTORIZATION THEOREM WITH APPLICATIONS TO INVARIANT SUBSPACES AND THE REFLEXIVITY OF ISOMETRIES

We prove a factorization result for spaces of vector-valued square integrable functions, and give two applications. The first one involves factorization results related to invariant subspaces of the Hardy space of the unit ball in C-d. The second application is a proof of the fact that arbitrary commutative families of isometries on a Hilbert space generate reflexive algebras.