Recent results on truncated Toeplitz operators

TL;DR

This survey reviews recent advances in understanding truncated Toeplitz operators, focusing on their boundedness, compactness, spectra, and related embedding measures, highlighting their mathematical properties and connections.

Contribution

It compiles and discusses recent results linking the properties of truncated Toeplitz operators to their symbols and embedding measures, providing a comprehensive overview.

Findings

Boundedness and compactness criteria established

Spectral properties characterized in relation to symbols

Connections made between operators and embedding measures

Abstract

Truncated Toeplitz operators are compressions of Toeplitz operators on model spaces; they have received much attention in the last years. This survey article presents several recent results, which relate boundedness, compactness, and spectra of these operators to properties of their symbols. We also connect these facts with properties of the natural embedding measures associated to these operators.