Products of Toeplitz Operators on the Polydisk
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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.
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