Partially isometric truncated and dual truncated Toeplitz operators

Abstract

Let $\hat{I}¸$ be a non-constant inner function and let $\ddot{I}•=\overline{u}v$, where $u$ and $v$ are inner functions such that $v$ divides $\hat{I}¸$. In this paper we characterize the partially isometric truncated Toeplitz operators $A_{\ddot{I}}•$ and dual truncated Toeplitz operators $D_{\ddot{I}}•$ with symbols of the form $\ddot{I}•=\overline{u}v$. Along with that, we obtain a few more characterization results, including the space of extremal vectors for non-zero partially isometric truncated and dual truncated Toeplitz operators.

Preliminary version. 13 pages