Abstract. We obtain a necessary and sufficient condition for a noninjective Toeplitz operator on $H^2$ of the unit disk to be surjective. The condition involves the extremal function for the kernel of the operator. The canonical right inverse of a surjective Toeplitz operator is shown to be a product of three Toeplitz operators.
AMS Subject Classification
(1991): 30D55, 46C07, 46E22, 47B32, 47B35
de Branges--Rovnyak spaces,
Received May 3, 2004. (Registered under 5834/2009.)