Szegő Limit Theorem for Truncated Toeplitz Operators

We discuss generalizations of the Szegő Limit Theorem to truncated Toeplitz operators. In particular, we consider compressions of Toeplitz operators to an increasing sequence of finite dimensional model spaces. We present two theorems. The first is a new variant of the Szegő Limit Theorem in this setting. The second relates to the variant given by Strouse-Timotin-Zarrabi in 2017, and characterizes the sequences for which that result holds.