Helton-Howe 迹、Connes-Chern 特征与量子化
泛函分析
2022-10-12 v2 复变函数
K理论与同调
摘要
我们通过量子化的思想研究加权 Bergman 空间上 Toeplitz 算子的 Helton-Howe 迹与 Connes-Chern 特征。当权趋于无穷时，我们证明了 Connes-Chern 特征在大 极限下的一个局部公式。并且我们表明 Toeplitz 算子的 Helton-Howe 迹独立于权 ，并利用调和分析与量子化给出了所有加权 Bergman 空间上 Helton-Howe 迹的局部公式。
引用
@article{arxiv.2204.04337,
title = {Helton-Howe Trace, Connes-Chern character and Quantization},
author = {Xiang Tang and Yi Wang and Dechao Zheng},
journal= {arXiv preprint arXiv:2204.04337},
year = {2022}
}
备注
72 pages, revised version. Version 1 of this article is split into two independent articles, Version 2 of arXiv:2204.04337 and arXiv:2210.04148. The main results of Version 1 of this article are presented in Version 2. And the results about trace of semicommutators on the unit disk together with related topics in Version 1 are included and generalized in a new paper, arXiv:2210.04148.