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arXiv · 0707.2025

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

M. Englis·K. Guo·G. Zhang
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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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M. Englis, K. Guo, G. Zhang. 2007-07-13. Toeplitz and Hankel operators and Dixmier traces on the unit ball of \mathbb C^n. https://arxiv.org/abs/0707.2025

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