Acta mathematica scientia,Series B ›› 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

 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).

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

CLC Number: 

  • 30D50
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