Integral Equations and Operator Theory

, Volume 45, Issue 4, pp 389–403

Products of Toeplitz Operators on the Polydisk

  • Xuanhao Ding
Research article

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. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations