On the Dilation of Truncated Toeplitz Operators

Abstract

An operator is called the dilation of a truncated Toeplitz operator if for two symbols and an inner function u, holds for where denotes the orthogonal projection of onto the model space and In this paper, we study properties of the dilation of truncated Toeplitz operators on . In particular, we provide conditions for the dilation of truncated Toeplitz operators to be normal. As some applications, we give several examples of such operators.