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 ${\Bbb C}^d$. The second application is a proof of the fact that arbitrary commutative families of isometries on a Hilbert space generate reflexive algebras.

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Published 1 January 1994