Toeplitz and Hankel operators and Dixmier traces on the unit ball of $\mathbb C^n$

Abstract

We compute the Dixmier trace of pseudo-Toeplitz operators on the Fock space. As an application we find a formula for the Dixmier trace of the product of commutators of Toeplitz operators on the Hardy and weighted Bergman spaces on the unit ball of <!-- MATH $\mathbb{C}^d$ --> . This generalizes an earlier work of Helton-Howe for the usual trace of the anti-symmetrization of Toeplitz operators.