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
Keyword(s):
{Toeplitz operators,
Devinatz--Widom theorem,
de Branges--Rovnyak spaces,
reproducing kernels,
Helson--Szegő weight,
extremal function}
Received May 3, 2004. (Registered under 5834/2009.)
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