n维单位球面上的Toeplitz符号演算(英文)  

Toeplitz Symbol Calculus on the Unit Sphere in C^n

作　　者：孔德芳[1] 徐宪民[1] 

机构地区：[1]嘉兴学院数学研究所,浙江嘉兴314001

出　　处：《应用泛函分析学报》2008年第4期298-304,共7页Acta Analysis Functionalis Applicata

基　　金：Supported by National Natural Science Foundation of China(10371051);Natural Science Foundation of Zhejiang Province(M103072);Jiaxing University Research Subject(70108002)

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{T_(?),(?)∈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(?)(称为丁的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.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.

关 键 词：HARDY空间 TOEPLITZ算子 BEREZIN变换 半交换子理想 

分 类 号：O177.1[理学—数学]