Research article

Integral Equations and Operator Theory

, Volume 45, Issue 4, pp 389-403

First online:

Products of Toeplitz Operators on the Polydisk

  • Xuanhao DingAffiliated withDepartment of Mathematics, Guilin Institute of Electronic Technology, Guilin 541004; People's Republic of China; E-mail: dxh@gliet.edu.cn

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Abstract.

This paper studies products of Toeplitz operators on the Hardy space of the polydisk. We show that T f T g = 0 if and only if T f T g is a finite rank if and only if T f or T g is zero. The product T f T g is still a Toeplitz operator if and only if there is a h $ \in $ L $ \infty $ (T n ) such that T f T g - T h 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.