Schatten-class Truncated Toeplitz Operators

TL;DR

This paper characterizes Schatten-class truncated Toeplitz operators, especially with analytic symbols or Hilbert-Schmidt class, and explores their properties in various model spaces and symbol classes.

Contribution

It provides a complete characterization of Schatten-class truncated Toeplitz operators with analytic symbols and those in the Hilbert-Schmidt class, expanding understanding of their structure.

Findings

Characterization of Schatten-class truncated Toeplitz operators with analytic symbols

Complete description of Hilbert-Schmidt truncated Toeplitz operators

Analysis of operators in model spaces generated by Blaschke products and singular inner functions

Abstract

We investigate truncated Toeplitz operators belonging to the Schatten ideals. We completely characterize such operators when they have an analytic symbol or belong to the ideal of Hilbert-Schmidt operators. We also study model spaces generated by Blaschke products associated with thin sequences, model spaces generated by certain types of singular inner functions, and operators associated with a class of very smooth symbols.