Unitary equivalence to truncated Toeplitz operators

In this paper we investigate operators unitarily equivalent to trun- cated Toeplitz operators. We show that this class contains certain sums of tensor products of truncated Toeplitz operators. In particular, it contains arbitrary inflations of truncated Toeplitz operators; this answers a question posed in (4). model spaces, are a generalization of the operators associated with Toeplitz matri- ces. They are introduced and discussed in great detail in a recent survey paper by Sarason (10). Some special cases have appeared long ago in the literature: the model operators for contractions with defect number one as well as their commutant are truncated Toeplitz operators with analytic symbols (see, for instance, (9, 11, 8)). This is a new area of study, and many simple questions remain open. The basic reference for this subject is (10), subsequent work is done in (4, 6, 3, 2).