Factorizations of characteristic functions
Journal of Operator Theory
Let A = (A1,..., An) and B = (B1,..., Bn) be row contractions on Hilbert spaces H1 and H2, respectively, and L be a contraction from Db = ranDB to DA* = ranDA*, where DB = (I - B*B)1/2 and DA*, = (I - AA*)1/2. Let ΘT be the characteristic function of T = Then ΘT coincides with the product of the characteristic function ΘA of A, the Julia-Halmos matrix corresponding to L and the characteristic function ΘB of B. More precisely, ΘT coincides with where Γ is the full Fock space. Similar results hold for constrained row contractions.
Haria, Kalpesh J.; Maji, Amit; and Sarkar, Jaydeb, "Factorizations of characteristic functions" (2017). Journal Articles. 2655.