The semi-commutator of Toeplitz operators on the bidisc

Details The semi-commutator of Toeplitz operators on the bidisc The semi-commutator of Toeplitz operators on the bidisc

1996-05-22

arxiv.org/abs/math/9605226v1

Mathematics

Functional Analysis

Scientific paper

In this paper we characterize when the semi-commutator $T_fT_g-T_{fg}$ of
two Toeplitz operators $T_f$ and $T_g$ 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 $T^2$ are given.

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