Journal of Operator Theory

Volume 38, Issue 1, Summer 1997 pp. 173-193.

The semi-commutator of Toeplitz operators on the bidisc

Authors: Caixing Gu

$1$ and Dechao Zheng

$2$
Author institution:

$1$ Department of Mathematics, California Polytechnic State University, San Luis Obispo, CA 93407, U.S.A.

$2$ Department of Mathematics, Vanderbilt University, Nashville, TN 37240, U.S.A.

Summary: In this paper we characterize when the semi-commutator T_f T_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 finite rank semi-commutator on the bidisc. Furthermore explicit examples of compact semi-commutators with symbols continuous on the bitorus

$\mathbb T^2$ are given.

Keywords: Toeplitz operators, Hankel operators, semi-commutators, bidisc.

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