  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 \mathbb C^d. This generalizes an earlier work of Helton-Howe
for the usual trace of the anti-symmetrization of Toeplitz operators.
