Shift invariant subspaces in the vector-valued Hardy space H 2 (E) play important roles in Nagy-Foias operator model theory. A theorem by Beurling, Lax and Halmos characterizes such invariant subspaces by operatorvalued inner functions Θ(z). When E = H 2 (D), H 2 (E) is the Hardy space over the bidisk H 2 (D 2 ). This paper shows that for some well-known examples of invariant subspaces in H 2 (D 2 ), the function Θ(z) turns out to be strikingly simple.
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