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Let S(z1;z2), S1(z1;z2) and S2(z1;z2) be power series with operator coe-cients such that S(z1;z2) = S1(z1;z2)S2(z1;z2). Assume that the multiplications by S1(z1;z2) and S2(z1;z2) are contractive transformations in H(D 2 ;C). Then the factorizations of spaces D(D; ~ S) and D(D 2 ;S) are well-behaved.

FACTORIZATION OF A HILBERT SPACE ON THE BIDISK