EQUIVALENCE CLASSES OF MIXED INVARIANTSUBSPACES OVER THE BIDISK

摘要

A closed subspace N of the Hardy space H2 over the bidisk is saidto be mixed invariant under T_zandT_w~*ifT_zNNandT_NN.In thispaper, we study unitary, similar and quasi-similar module maps for mixed invariantsubspaces. We give some characterization of these maps. All unitary modulemaps are multiplication operators of unimodular functions. Under the conditiondim(N zN) = 1, we can describe similar and quasi-similar module maps byouter functions.