Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

NOTE ON COMMUTING TOEPLITZ OPERATORS ON THE PLURIHARMONIC BERGMAN SPACE

  • Published : 2006.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

We obtain a characterization of commuting Toeplitz operators with holomorphic symbols acting on the pluriharmonic Bergman space of the polydisk. We also obtain a characterization of normal Toeplitz operators with pluriharmonic symbols. In addition, some results for special types of semi-commutators are included.

Keywords

References

  1. S. Axler and Z. Cuckovid, Commuting Toeplitz operators with harmonic symbols, Integral Equations Operator Theory, 14 (1991), no. 1, 1-12 https://doi.org/10.1007/BF01194925
  2. B. R. Choe, H. Koo, and Y. J. Lee, Commuting Toeplitz operators on the polydisk, Trans. Amer. Math. Soc. 356 (2004), no. 5, 1727-1749 https://doi.org/10.1090/S0002-9947-03-03430-5
  3. B. R. Choe and Y. J. Lee, Commuting Toeplitz operators on the harmonic Bergman space, Michigan Math. J. 46 (1999), no. 1, 163-174 https://doi.org/10.1307/mmj/1030132367
  4. Z. Cuckovic, Commuting Toeplitz operators on the Bergman space of an annulus, Michigan Math. J. 43 (1996), no. 2, 355-365 https://doi.org/10.1307/mmj/1029005468
  5. S. G. Krantz, Function theory of several complex variables, John Wiley and Sons, New York, 1982
  6. Y. J. Lee and K. Zhu, Some differential and integral equations with applications to Toeplitz operators, Integral Equations Operator Theory 44 (2002), 466-479 https://doi.org/10.1007/BF01193672
  7. W. Rudin, Function theory in the unit ball of en, Springer-Verlag, Berlin, Heidelberg, New York, 1980
  8. S. Sun and D. Zheng, Toeplitz operators on the polydisk, Proc. Amer. Math. Soc. 124 (1996), no. 11, 3351-3356
  9. D. Zheng, Commuting Toeplitz operators with pluriharmonic symbols, Trans. Amer. Math. Soc. 350 (1998), no. 4, 1595-1618 https://doi.org/10.1090/S0002-9947-98-02051-0
  10. K. Zhu, Operator theory in function spaces, Marcel Dekker, New York, 1990

Cited by

  1. Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball vol.2016, 2016, https://doi.org/10.1155/2016/1054768
  2. Commuting dual Toeplitz operators on the harmonic Bergman space vol.58, pp.7, 2015, https://doi.org/10.1007/s11425-014-4940-x
  3. The Pluriharmonic Hardy Space and Toeplitz Operators 2017, https://doi.org/10.1007/s00025-017-0728-y
  4. The Numerical Range of Toeplitz Operator on the Polydisk vol.2009, 2009, https://doi.org/10.1155/2009/757964
  5. Commuting dual Toeplitz operators on the harmonic Dirichlet space vol.32, pp.9, 2016, https://doi.org/10.1007/s10114-016-5663-4
  6. Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space vol.2013, 2013, https://doi.org/10.1155/2013/578436
  7. Commuting Toeplitz operators on the hardy space of the polydisk vol.31, pp.4, 2015, https://doi.org/10.1007/s10114-015-4174-z