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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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