数学物理学报 ›› 2011, Vol. 31 ›› Issue (6): 1550-1558.

• 论文 • 上一篇    下一篇

单位球向量值Bergman空间上的Toeplitz乘积

于涛, 朱若卫   

  1. 浙江师范大学 数学系 |浙江金华 321004
  • 收稿日期:2010-04-29 修回日期:2011-10-18 出版日期:2011-12-25 发布日期:2011-12-25
  • 基金资助:

    国家自然科学基金(10971195, 10771064)和浙江省自然科学基金(Y6090689, Y6110260)资助

Toeplitz Products on Vector-valued Bergman Spaces of the Unit Ball

 YU Thao, ZHU Ruo-Wei   

  1. Department of Mathematics, Zhejiang Normal University, Zhejiang Jinhua 310028
  • Received:2010-04-29 Revised:2011-10-18 Online:2011-12-25 Published:2011-12-25
  • Supported by:

    国家自然科学基金(10971195, 10771064)和浙江省自然科学基金(Y6090689, Y6110260)资助

摘要:

FG是函数组成的矩阵, 它们的元素都是单位球上平方可积的解析函数, 该文研究单位球向量值Bergman空间上的Toeplitz算子乘积TFTG*, 分别获得了算子TFTG*有界的充分条件和必要条件.

关键词: 向量值Bergman空间, Toeplitz算子, Berezin变换,

Abstract:

In this paper the authors  obtain a sufficient condition and a necessary condition for the Toeplitz product TFTG* on vector-valued Bergman spaces of the unit ball to be bounded respectively, where F and G are matrices which entries are square-integrable and analytic functions on the unit ball.

Key words: Vector-valued Bergman space, Toeplitz operator, Berezin transform, Trace

中图分类号: 

  • 47B35