Blaschke products and the rank of backward shift invariant subspaces over the bidisk

Let H2(D2) be the Hardy space over the bidisk. For sequences of Blaschke products {ϕn(z): −∞ < n < ∞} and {ψn(w): −∞ < n < ∞} satisfying some additional conditions, we may define a Rudin type invariant subspaceM. We shall determine the rank of H2(D2) Mfor the pair of operators T ∗ z and T ∗ w. © 2011 Elsevier Inc. All rights reserved