Cross Commutators on Backward Shift Invariant Subspaces over the Bidisk
by
Kei Ji Izuchi
Niigata University, Japan
Coauthors: Kou Hei Izuchi

Let M be an invariant subspace of H² = H²(G²) the Hardy space over the bidisk G² with M ≠ {0} and M ≠ H². We write N=H²\ominus M. For y ∈ L^∞, we define the operators R_y on M and S_y on N by R_y f = P_M(yf) and S_y f=P_N(yf), respectively. We talk about the commutativity of R_y1(z), R^*_y2(w) and S_y1(z), S^*_y2(w), respectively.

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Date received: January 15, 2008