Advertisement

Commuting dual Toeplitz operators on weighted Bergman spaces of the unit ball

  • Yu Feng Lu
  • Jun Yang
Article

Abstract

In this paper, we study the commutativity of dual Toeplitz operators on weighted Bergman spaces of the unit ball. We obtain the necessary and sufficient conditions for the commutativity, essential commutativity and essential semi-commutativity of dual Toeplitz operator on the weighted Bergman spaces of the unit ball.

Keywords

Dual Toeplitz operator unit ball weighted Bergman space commutativity 

MR(2000) Subject Classification

47B35 47B47 

References

  1. [1]
    Brown, A., Haloms, P. R.: Algebraic properties of Toeplitz operators. J. Reine Angew. Math., 213, 89–102 (1964)MathSciNetGoogle Scholar
  2. [2]
    Axler, S., Čučković, Z.: Commuting Toeplitz operators with harmonic symbols. Integr. Equ. Oper. Theory, 14, 1–12 (1991)MATHCrossRefGoogle Scholar
  3. [3]
    Stroethoff, K.: Essentially commuting Toeplitz oprtators with harmonic symbols. Canada. J. Math., 45, 1080–1993 (1993)MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Axler, S., Čučković, Z., Rao, N. V.: Commuting of analytic Toeplitz operators on the Bergman space. Proc. Amer. Math. Soc., 128, 1951–1953 (2000)MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Zheng, D.: Commuting Toeplitz operators with pluriharmonic symbols. Trans. Amer. Math. Soc., 350, 1595–1618 (1998)MathSciNetCrossRefGoogle Scholar
  6. [6]
    Choe, B. R., Lee, Y. J.: Pluriharmonic symbols of commuting Toeplitz operators. Illinois J. Math., 37, 424–436 (1993)MathSciNetMATHGoogle Scholar
  7. [7]
    Choe, B. R., Lee, Y. J.: Pluriharmonic symbols of essentially commuting Toeplitz operators. Illinois J. Math., 42, 280–293 (1998)MathSciNetMATHGoogle Scholar
  8. [8]
    Lee, Y. J.: Pluriharmonic symbols of commuting Toeplitz type operators on the weighted Bergman spaces. Canad. Math. Bull., 41, 129–136 (1998)MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    Lu, Y. F.: Commuting of Toeplitz oerators on the Bergman space of the bidisc. Bull. Austral. Math. Soc., 66, 345–351 (2002)MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    Choe, B. R., Koo, H., Lee, Y. J.: Commuting Toeplitz operators on the polydisk. Trans. Amer. Math. Soc., 356, 1727–1749 (2002)MathSciNetCrossRefGoogle Scholar
  11. [11]
    Stroethoff, K., Zheng, D.: Algebraic and spectral properties of dual Toeplitz operators. Trans. Amer. Math. Soc., 354, 2495–2520 (2002)MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    Lu, Y. F.: Commuting dual Toeplitz operators with pluriharmonic symbols. J. Math. Anal. Appl., 302, 149–156 (2005)MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    Lu, Y. F., Shang, X. S.: Commuting dual Toeplitz operators on the polydisk. Acta Mathematica Sinica, English Series, 23, 857–868 (2007)MathSciNetMATHCrossRefGoogle Scholar
  14. [14]
    Zhu, K.: Spaces of Holomorphic Functions in the Unit Ball, Springer-Verlag, New York, 2004Google Scholar
  15. [15]
    Rudin, W.: Function Theory in the Unit Ball in C n, Springer-Verlag, New York, 1980MATHGoogle Scholar
  16. [16]
    Stroethoff, K., Zheng, D.: Bounded Toeplitz products on Bergman spaces of the unit ball. J. Math. Anal. Appl., 325, 114–129 (2007)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianP. R. China
  2. 2.College of Arts and ScienceShanghai Maritime UniversityShanghaiP. R. China

Personalised recommendations