On Schatten-class perturbations of Toeplitz operators

TL;DR

This paper characterizes the commutant of analytic Toeplitz operators modulo Schatten-p-class operators on multivariable domains, extending known results from the unit disc to more complex domains.

Contribution

It generalizes Xia's result on compact perturbations of Toeplitz operators to Schatten-p-class perturbations on multivariable domains.

Findings

The commutant characterization extends to Schatten-p-class operators.

Results hold on strictly pseudoconvex and symmetric domains in C^n.

The classical compact case is a special instance of the Schatten-p-class case.

Abstract

We characterize the commutant of the analytic Toeplitz operators modulo operators of Schatten-p-class on suitable multivariable domains. We show that a result of J. Xia on compact perturbations of Toeplitz operators on the unit disc remains true on strictly pseudoconvex and symmetric domains in C^n if the ideal of compact operators is replaced by the Schatten-p-classes with p strictly less than infinity.