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n维单位球面上的Toeplitz符号演算

ISSN号：1000-0917
期刊名称：《数学进展》
时间：0
分类：O177.1[理学—数学;理学—基础数学]
作者机构：[1]嘉兴学院数学研究所,浙江嘉兴314001
相关基金：Foundation item： Supported by National Natural Science Foundation of China （10371051）; Natural Science Foundation of Zhejiang Province（M103072） ; Jiaxing University Research Subject （70108002）.Acknowledgement The authors would like to Lemma 2.6 in this paper. The authors would also thank M. Englis for his excellent proof of like to thank Professor Sun Shunhua, Yan Congquan and Hu Junyun for their various helpful suggestions.

关键词： HARDY空间, TOEPLITZ算子, BEREZIN变换, 半交换子理想, Hardy space, Toeplitz operator, Berezin transform, semicommutator ideal

中文摘要：

探讨了C^n中单位球面S上Berezin变换和Toeplitz算子的性质，证明了由{Tφ,φ∈L^∞ （S）}所生成的C^＊-代数中算子T的符号恰好为单位球B上函数T（称为T的Berezin变换）的非切向边界值．此外，本文还得到了经典Toeplitz符号演算的有趣推广．

英文摘要：

We investigate the properties of Berezin transform and Toeplitz operators on the unit sphere S in C^n. We obtain the symbol of an operator T in the C^n-algebra I（L^∞ （S）） generated by {Tφ,φ∈L^∞ （S）} as the nontangential boundary value of a certain function T （called the Berezin transform of T） on the unit ball B. Furthermore, we construct interesting extensions of the classical Toeplitz symbol calculus for Toeplitz operators to larger operator algebras.

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