Abstract. Considering a completely non-unitary contraction whose defect space, together to that of the adjoint, have dimension 2, we study its perturbations obtained by modifying the action on the defect spaces. we determine when the resulting contraction is also completely non-unitary. As an application, a theorem of De Branges about entire functions is recaptured in a completely different context.

AMS Subject Classification (1991): 47A45, 47A55

Received December 28, 1993, and in revised form February 20, 1995. (Registered under 5699/2009.)