Toeplitz and Hankel operators and Dixmier traces on the unit ball of \mathbb C^n
M. Englis, K. Guo, G. Zhang
TL;DR
This paper computes the Dixmier trace for pseudo-Toeplitz operators on Fock space and derives a formula for the trace of products of commutators of Toeplitz operators on Hardy and Bergman spaces in the unit ball of complex space.
Contribution
It generalizes previous results by providing a new formula for the Dixmier trace of Toeplitz operator products on several function spaces.
Findings
Dixmier trace of pseudo-Toeplitz operators computed
Formula for Dixmier trace of commutator products derived
Generalizes Helton-Howe's earlier work
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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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Harmonic Analysis Research · Geometric Analysis and Curvature Flows