On Schatten-class perturbations of Toeplitz operators

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.