In the theory of analytic characteristic functions (c.f.'s), it is well-known that: (1) the order of an entire c.f. cannot be less than unity, unless the function is identically equal to one (P. Lévy) ...

Let A = (A₁,...,An) and B = (B₁,...,Bn) be row contractions on Hilbert spaces 𝓗₁ and 𝓗₂, respectively, and L be a contraction from D B = ran ¯ D B to D A * = ran ¯ D A * where DB = (I – B*B)1/2 and ...