数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (2): 434-440.doi: 10.1016/S0252-9602(11)60243-9

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CYCLIC VECTORS AND CELLULAR INDECOMPOSABLE OPERATORS ON Qp SPACES

叶善力|娄增建*   

  1. 1. Department of Mathematics, Fujian Normal University, Fuzhou 350007, China
    2. Department of Mathematics, Shantou University, Shantou 515063, China
  • 收稿日期:2008-05-13 修回日期:2009-10-05 出版日期:2011-03-20 发布日期:2011-03-20
  • 通讯作者: 娄增建 E-mail:shanliye@fjnu.edu.cn; zjlou@stu.edu.cn
  • 基金资助:

    This article was supported by NNSF of China (10771130), Specialized Research Fund for the Doctoral Program of High Education (2007056004), NSF of Guangdong Province (10151503101000025), and NSF of Fujian Province (2009J01004).

CYCLIC VECTORS AND CELLULAR INDECOMPOSABLE OPERATORS ON Qp SPACES

 YE Shan-Li, LOU Zeng-Jian*   

  1. 1. Department of Mathematics, Fujian Normal University, Fuzhou 350007, China
    2. Department of Mathematics, Shantou University, Shantou 515063, China
  • Received:2008-05-13 Revised:2009-10-05 Online:2011-03-20 Published:2011-03-20
  • Contact: LOU Zeng-Jian E-mail:shanliye@fjnu.edu.cn; zjlou@stu.edu.cn
  • Supported by:

    This article was supported by NNSF of China (10771130), Specialized Research Fund for the Doctoral Program of High Education (2007056004), NSF of Guangdong Province (10151503101000025), and NSF of Fujian Province (2009J01004).

摘要:

We identify the functions whose polynomial multiples are weak* dense in Qp spaces and prove that if |f(z)|≥|g(z)| and g is cyclic in Qp, then f is cyclic in Qp. We also show that the multiplication operator Mz on Qp spaces is cellular indecomposable.

关键词: Cyclic vectors, Outer functions, Cellular indecomposable,  Qp spaces

Abstract:

We identify the functions whose polynomial multiples are weak* dense in Qp spaces and prove that if |f(z)|≥|g(z)| and g is cyclic in Qp, then f is cyclic in Qp. We also show that the multiplication operator Mz on Qp spaces is cellular indecomposable.

Key words: Cyclic vectors, Outer functions, Cellular indecomposable,  Qp spaces

中图分类号: 

  • 30D50