Trace Formula of Semicommutators

Xiang Tang; Yi Wang; Dechao Zheng

Trace Formula of Semicommutators

Complex Variables 2022-10-12 v1 Functional Analysis K-Theory and Homology

Authors: Xiang Tang , Yi Wang , Dechao Zheng

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.

Keywords

trace formula toeplitz operators bergman spaces

Cite

@article{arxiv.2210.04148,
  title  = {Trace Formula of Semicommutators},
  author = {Xiang Tang and Yi Wang and Dechao Zheng},
  journal= {arXiv preprint arXiv:2210.04148},
  year   = {2022}
}

Comments

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 $\mathbb{C}^n$

Trace Formula of Semicommutators

Abstract

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