中山大学学报自然科学版 ›› 2016, Vol. 55 ›› Issue (6): 74-78.

• 研究论文 • 上一篇    下一篇

单位球Dirichlet空间上的紧Toeplitz算子

陈建军1,2,王晓峰3   

  1. 1. 肇庆学院数学与统计学院, 广东 肇庆 526061;
    2. 中山大学数学学院, 广东 广州 510275;
    3. 广州大学数学与信息科学学院,数学与交叉科学广东普通高校重点实验室, 广东 广州 510006
  • 收稿日期:2015-12-08 出版日期:2016-11-25 发布日期:2016-11-25
  • 通讯作者: 王晓峰;E-mail:wangxiaofeng514@hotmail.com

Compact Toeplitz operators on the Dirichlet space over unit ball

CHEN Jianjun1,2,WANG Xiaofeng3   

  1. 1. School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China;
    2. School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China;
    3. School of Mathematics and Information Science and Key Laboratory of Mathematics and Interdisciplinary Sciences of the Guangdong Higher Education Institute, Guangzhou University, Guangzhou 510006, China
  • Received:2015-12-08 Online:2016-11-25 Published:2016-11-25

摘要:

研究单位球上Dirichlet空间上的Toeplitz算子的紧性,得到结论:有限个具有有界符号的Toeplitz算子乘积的有限和是一个紧算子,等价于它的Berezin型变换消失于单位球面。

关键词: Toeplitz算子, Berezin型变换, Dirichlet空间, 单位球

Abstract:

The compactness of Toeplitz operators on Dirichlet space is studied. It is proved that finite sums of finite products of Toeplitz operators with bounded symbols are compact if and only if their Berezin-type transforms vanish on the boundary of the unit ball.

Key words: Toeplitz operator, Berezin type transform, Dirichlet space, unit ball

中图分类号: