Toeplitz and Hankel operators and Dixmier traces on the unit ball of ℂⁿ

Engliš, Miroslav; Guo, Kunyu; Zhang, Genkai

doi:10.1090/S0002-9939-09-09331-9

Toeplitz and Hankel operators and Dixmier traces on the unit ball of $\mathbb C^n$
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by Miroslav Engliš, Kunyu Guo and Genkai Zhang

Proc. Amer. Math. Soc. 137 (2009), 3669-3678

DOI: https://doi.org/10.1090/S0002-9939-09-09331-9

Published electronically: June 16, 2009

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

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