On Schatten-class perturbations of Toeplitz operators

Original · EN

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 Cⁿ if the ideal of compact operators is replaced by the Schatten-p-classes with p strictly less than infinity.