We discuss generalizations of the Szeg{o} 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 Szeg{o} 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.
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Miheisi et al. (2024) studied this question.
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