摘要
本文刻画了C^n中单位球和多圆盘Bergman空间上一些Toeplitz算子的换位。首先,对双圆盘Bergman空间,刻画了什么时候 Toeplitz算子T_f和T_g交换,这里 f=f1+,g=g1+,fi,gi∈H~∞(D^2)(i=1,2)。其次,如果表示由多复变量 Toeplitz算子生成的赋范闭子代数,证明了对每个正整数m,{T_z_1~m,…,T_z_n^m}′∩是所有解析Toeplitz算子的集合,这里z_i(i=1,…,n)是坐标函数。
This paper describes commutants of some Toeplitz operators on the Bergman space of the unit ball and the polydisk in Cn. First, on the Bergman space of the bidisk, the author describes when Toeplitz operators Tf and Tg commute, where f = f1 + f2, g = g1 + f2, fi,gi ∈ H∞(D2) (i = 1,2). Secondly, if denote the norm closed subalgebra generated by Toeplitz operators in several complex variables, the author shows that for each positive integer m, {Tz1m, …, Tznm}' ∩ is the set of all analytic Toeplitz operator, where zi (i = 1, …???,n} is the coordinate function.
出处
《数学年刊（A辑）》
CSCD
北大核心
2003年第4期437-444,共8页
Chinese Annals of Mathematics
基金
国防科工委基础科研资助的项目
