Abstract. The space ${\cal H}ank$ of Hankel operators acting on the Hardy space ${\bf H}^2$ is a module over ${\bf H}^\infty $. There is a natural correspondence between weak* closed submodules of ${\cal H}ank$ and individual inner functions, and we apply work of V. Kapustin on Jordan models to characterize which submodules are reflexive in terms of the canonical factorization of these functions. We also prove that reflexivity of any weak* closed subspace of ${\cal H}ank$ is equivalent to reflexivity of the largest ${\bf H}^\infty $ module it contains. Analogous results are obtained in the finite dimensional and ``semi-infinite'' dimensional settings.

AMS Subject Classification (1991): 47B35, 47L05, 47A15, 46E15, 47A60

Received August 15, 2006. (Registered under 6457/2009.)