Multipliers and equivalences between Toeplitz kernels

TL;DR

This paper characterizes multipliers between Toeplitz kernels using test functions and maximal vectors, explores their applications to model spaces, and analyzes conditions for kernel equivalences, advancing understanding of Toeplitz operator structures.

Contribution

It introduces a new characterization of Toeplitz kernel multipliers via maximal vectors and inner-outer factorizations, with applications to model spaces and kernel equivalences.

Findings

Characterization of multipliers using test functions and maximal vectors

Parametrization of maximal vectors through inner-outer factorizations

Analysis of surjective multipliers and kernel equivalences

Abstract

Multipliers between kernels of Toeplitz operators are characterised in terms of test functions (so-called maximal vectors for the kernels); these maximal vectors may easily be parametrised in terms of inner and outer factorizations. Immediate applications to model spaces are derived. The case of surjective multipliers is also analysed. These ideas are applied to describing equivalences between two Toeplitz kernels.