Bergman空间上的复合算子的范数  

Norms of Composition Operators on the Bergman Space

作　　者：王茂发[1] 刘培德[1] 

机构地区：[1]武汉大学数学与统计学院,武汉430072

出　　处：《数学学报（中文版）》2004年第2期365-370,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(19771063)

摘　　要：本文研究了Bergman空间上的复合算子的范数与再生核的关系,证明了紧复合算子C的范数‖C‖=sup{‖C*kw‖:w∈D}的充要条件是(0)=0或是仿射映射,即(z)=sz+t,s,t是满足|s|+|t|<1的常数,其中kw为Bergman空间的规范再生核, C*是C的共轭算子.In this paper, we study the connection between norms of composition operators on the Bergman space and the reproducing kernels. It is shown that when C is compact then the action of its adjoint C* on the set of normalized reproducing kernels of Bergman space determines the norm of C if and only if (0) = 0 or has the affine form z → sz +t for some constants s and t satisfying |s |+ |t| < 1.

关 键 词：BERGMAN空间 复合算子 Bergman再生核 

分 类 号：O174.5[理学—数学]