The semi-commutator of Toeplitz operators on the bidisc
Caixing Gu, Dechao Zheng
Abstract
In this paper we characterize when the semi-commutator TfTg-Tfg of two Toeplitz operators Tf and Tg on the Hardy space of the bidisc is zero. We also show that there is no nonzero finite rank semi-commutator on the bidisc. Furthermore explicit examples of compact semi-commutators with symbols continuous on the bitorus T2 are given.
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