加权Dirichlet空间上紧Toeplitz算子  

Compact Toeplitz Operators on Weighted Dirichlet Space

作　　者：王晓峰[1] 夏锦[1] 

机构地区：[1]广州大学数学与信息科学学院,广东广州510006

出　　处：《四川师范大学学报（自然科学版）》2010年第1期36-41,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(1067042);教育部博士点基金资助项目

摘　　要：对α>-1,若算子S是加权Dirichlet空间Dα上有限个Toeplitz算子乘积的有限和,利用不同于加权Dirichlet空间再生核的一种新奇异积分核,得到了S为紧算子的充要条件是当z趋于单位圆盘边界时,S的类Berezin变换趋于0.又利用与Bermgan空间不同的酉算子Uz,定义了算子乘积Sz=UzSUz,得到S为紧算子的充要条件是当z趋于单位圆盘边界时,Szw在D内弱收敛到0.Let α-1 and S be a finite sum of finite products of Toeplitz operators in a weighted Dirichlet space Dα.By using a new singular integral kernel which is different from the recovery kernel in weighted Dirichlet space,it is proved that S is compact if and only if the Berezin transformation tends to 0 as z goes to the boundary of the unit disk.Furthermore,an operator product Sz=UzSUz is defined,where Uz is the unitary operator which is different from that in Bergman space.It is proved that S is compact if and only if Szw is weakly converged to 0 as z goes to the boundary of the unit disk.

关 键 词：加权DIRICHLET空间 TOEPLITZ算子 紧算子 

分 类 号：O177[理学—数学]