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

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

2007-07-13

arxiv.org/abs/0707.2025v1

Mathematics

Complex Variables

Proc. Amer. Math. Soc. to appear

Scientific paper

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.

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