# A Szeg\"o type theorem for truncated Toeplitz operators

## TL;DR

This paper establishes Szeg"o type theorems describing the asymptotic behavior of truncated Toeplitz operators when compressed to an increasing sequence of finite-dimensional model spaces, advancing understanding of their spectral properties.

## Contribution

It introduces Szeg"o type asymptotic results specifically for truncated Toeplitz operators on model spaces, a novel extension in operator theory.

## Key findings

- Asymptotic formulas for truncated Toeplitz operators derived
- Spectral behavior characterized for increasing chain of model spaces
- New Szeg"o type theorems proved for this class of operators

## Abstract

Truncated Toeplitz operators are compressions of multiplication operators on $L^2$ to model spaces (that is, subspaces of $H^2$ which are invariant with respect to the backward shift). For this class of operators we prove certain Szeg\"o type theorems concerning the asymptotics of their compressions to an increasing chain of finite dimensional model spaces.