Toeplitz kernels and model spaces

TL;DR

This paper reviews classical and recent results on Toeplitz kernels and their connection to model spaces, emphasizing the importance of maximal vectors in understanding these kernels.

Contribution

It provides a comprehensive overview of Toeplitz kernels and model spaces, highlighting the role of maximal vectors in their structure and relationships.

Findings

Maximal vectors are fundamental in the structure of Toeplitz kernels.

Model spaces are special Toeplitz kernels with unique properties.

The review connects classical and recent developments in the theory.

Abstract

We review some classical and more recent results concerning kernels of Toeplitz operators and their relations with model spaces, which are themselves Toeplitz kernels of a special kind. We highlight the fundamental role played by the existence of maximal vectors for every nontrivial Toeplitz kernel.