Trace Formula of Semicommutators
Abstract
For weighted Bergman spaces on the unit disk, we give trace formulas of semicommutators of Toeplitz operators with $\mathscr{C}^2(\overline{\mathbb{D}})$ symbols. We generalize this formula to weighted Bergman spaces on the unit ball in higher dimensions. Applications and examples on the Hankel operators are also discussed.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2022
- DOI:
- arXiv:
- arXiv:2210.04148
- Bibcode:
- 2022arXiv221004148T
- Keywords:
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- Mathematics - Complex Variables;
- Mathematics - Functional Analysis;
- Mathematics - K-Theory and Homology
- E-Print:
- 40 pages. This is an article independent of Version 2 of arXiv:2004.04337. This article together with Version 2 of arXiv:2004.04337 supersedes Version 1 of arXiv:2004.04337. The results on trace of semicommutators on the unit disk together with related topics in Version 1 of arXiv:2004.04337, are included in this article and generalized to unit balls in $\mathbb{C}^n$