Abstract. Nakazi, Seto, and the first author gave a characterization of backward shift invariant subspaces of the Hardy space over the bidisk on which the cross commutators $[S_z,S^*_w]$ and $[S_{z^2},S^*_w]$ vanish, respectively. A characterization is given of backward shift invariant subspaces on which $[S_{z^n},S^*_w] = 0$ for a positive integer $n\ge2$.
AMS Subject Classification
(1991): 47A15, 32A35
Keyword(s):
Hardy space,
backward shift invariant subspace,
cross commutator
Received December 13, 2005, and in revised form March 22, 2006. (Registered under 5920/2009.)
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