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Rank-One Cross Commutators on Backward Shift Invariant Subspaces on the Bidisk Kei Ji IZUCHI Kou Hei IZUCHI Abstract For a backward shift invariant subspace N in H~2(Γ~2),the operators S_z and S_w on N are defined by S_z=P_NT_(z|N) and S_w=P_NT_(w|N),where P_N is the orthogonal projection from L~2(Γ~2) onto N.We give a characterization of N satisfying rank[S_z,S_w~*]=1.
Rank-One Cross Commutators on Backward Shift Invariant Subspaces on the Bidisk Kei Ji IZUCHI Kou Hei IZUCHI Abstract For a backward shift invariant subspace N in H ~ 2 (Γ ~ 2), operators S_z and S_w on N are defined by S_z = P_NT_ (z | N) and S_w = P_NT_ (w | N), where P_N is the orthogonal projection from L ~ 2 (Γ ~ 2) onto N.We give a characterization of N satisfying rank [S_z, S_w ~ *] = 1 .