规范权Bergman空间上Toeplitz算子的本性范数  

Essential Norm of Toeplitz Operators on Bergman spaces with regular weights

作　　者：周立芳[1] 卢金 Li Fang ZHOU;Jin LU(Department of Mathematics,Huzhou University,Huzhou 313000,P.R.China;School of Internet,Anhui University,He'fei 230039,P.R.China)

机构地区：[1]湖州师范学院数学系,湖州313000 [2]安徽大学互联网学院,合肥230039

出　　处：《数学学报（中文版）》2022年第4期699-708,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11801172,11971165);浙江省自然科学基金资助项目(LY20A010007)。

摘　　要：设1 <p <∞,μ为p-Carleson测度,本文证明了规范权Bergman空间Aωp上非紧Toeplitz算子Tμ的本性范数等于其到紧Toeplitz算子集合的距离.更进一步,本文给出了此距离可以用无限个紧Toeplitz算子刻画.In this paper,for 1μwithμbeing a positive p-Carleson measure equals its distance to the set of compact Toeplitz operators on the Bergman space with regular weight Aωp.Moreover,the distance is realized by infinitely many compact Toeplitz operators.

关 键 词：BERGMAN空间 TOEPLITZ算子 本性范数 

分 类 号：O174.5[理学—数学]