Products of Toeplitz Operators on the Polydisk
- Cite this article as:
- Ding, X. Integr. equ. oper. theory (2003) 45: 389. doi:10.1007/s000200300013
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.