Abstract. In the previous paper, we gave a characterization of backward shift invariant subspaces of the Hardy space in the bidisc which satisfy the doubly commuting condition $S_zS^*_w = S^*_wS_z$ for the compression operators $S_z$ and $S_w$. In this paper, we give a characterization of backward shift invariant subspaces satisfying $S^2_zS^*_w = S^*_wS^2_z$.

AMS Subject Classification (1991): 47A15, 32A35

Keyword(s): Hardy space, backward shift, invariant subspace

Received March 24, 2004, and in revised form June 1, 2004. (Registered under 5842/2009.)