We study the convergence of a sequence of finite Blaschke products of a fix
order toward a rotation. This would enable us to get a better picture of a
characterization theorem for finite Blaschke products.
Compressions of Toeplitz operators to coinvariant subspaces of $H^2$ are
called \emph{truncated Toeplitz operators}. We study two questions related to
these operators. The first, raised by Sarason, is whether boundedness of the
operator implies the existence of a bounded symbol; the second is the
reproducing kernel thesis. We show that in general the answer to the first
question is negative, and we exhibit some classes of spaces for which the
answers to both questions are positive.
Compressions of Toeplitz operators to coinvariant subspaces of $H^2$ are
called \emph{truncated Toeplitz operators}. We study two questions related to
these operators. The first, raised by Sarason, is whether boundedness of the
operator implies the existence of a bounded symbol; the second is the
reproducing kernel thesis. We show that in general the answer to the first
question is negative, and we exhibit some classes of spaces for which the
answers to both questions are positive.