Integral Equations and Operator Theory

, Volume 45, Issue 4, pp 389–403

Products of Toeplitz Operators on the Polydisk

  • Xuanhao Ding
Research article

DOI: 10.1007/s000200300013

Cite this article as:
Ding, X. Integr. equ. oper. theory (2003) 45: 389. doi:10.1007/s000200300013

Abstract.

This paper studies products of Toeplitz operators on the Hardy space of the polydisk. We show that TfTg = 0 if and only if TfTg is a finite rank if and only if Tf or Tg is zero. The product TfTg is still a Toeplitz operator if and only if there is a h $ \in $ L $ \infty $(Tn) such that TfTg - Th is a finite rank operator. We also show that there are no compact simi-commutators with symbols pluriharmonic on the polydisk.

Keywords. Toeplitz operator, Hardy space, Polydisk.¶ Mathematics Subject Classification (2000). 47B35.

Copyright information

© Birkhäuser Verlag, Basel 2003

Authors and Affiliations

  • Xuanhao Ding
    • 1
  1. 1.Department of Mathematics, Guilin Institute of Electronic Technology, Guilin 541004; People's Republic of China; E-mail: dxh@gliet.edu.cnCN