Toeplitz operators on some function spaces

TL;DR

This paper provides new structure theorems for Toeplitz operators on various function spaces, improving understanding of their properties like hyponormality, subnormality, and divisibility.

Contribution

It introduces structure theorems that enhance previous results on Toeplitz operators, revealing conditions for subnormality and other restrictive classes.

Findings

Operators or their adjoints are often subnormal or moment infinitely divisible.

The structure theorems improve and extend previous results on hyponormality and contractivity.

Recovers and enhances classical results on Toeplitz operators on Bergman and Hardy spaces.

Abstract

We reconsider studies of Toeplitz operators on function spaces (the weighted Bergman space, the generalized derivative Hardy space) and the H-Toeplitz operators on the Bergman space. Past studies have considered the presence or absence of hyponormality or questions of contractivity or expansivity; we provide structure theorems for these operators that allow us to recapture, and often considerably improve, these results. In some cases these operators or their adjoints are actually in more restrictive classes, such as subnormal or moment infinitely divisible ($\mathcal{MID}$).