Journal of Operator Theory

Volume 59, Issue 1, Winter 2008 pp. 3-28.

On Toeplitz operators similar to isometries

Authors: Maria F. Gamal'
Author institution: St. Petersburg Division of the Steklov Mathematical Institute, Fontanka, 27, 191023 St. Petersburg, Russia

Summary: Let

$T$ be a Toeplitz operator on the Hardy space

$H^2$ on the unit circle, and let the symbol of

$T$ be of the form

$\frac{\varphi}{\psi}$ , where

$\varphi$ is inner function,

$\psi$ is a finite Blaschke product, and

$\deg\psi\leqslant\deg\varphi$ . D.N.~Clark proved that such

$T$ is similar to an isometry. In this paper, we find this isometry.

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