Abstract
In this paper we completely characterize when the commutator and semi-commutator of two monomial-type Toeplitz operators on the Fock space over ℂn have finite rank. In sharp contrast to Bergman space over the unit ball case, it turns out that there are many other cases on the Fock space for (semi-)commuting Toeplitz operators.
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Acknowledgement
The author would like to thank the referee for valuable comments and suggestions that considerably improved the paper’s presentation. This paper was completed while the author visited the Department of Mathematics and Statistics at the State University of New York at Albany. The author also wish to thank SUNY-Albany for hosting the visit and thank the China Scholarship Council for financial support.
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Dong was supported in part by the National Natural Science Foundation of China (Grant Nos. 11201331; 11771323).
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Dong, XT. Commutators and Semi-Commutators of Toeplitz Operators on the Fock Space. Indian J Pure Appl Math 51, 195–215 (2020). https://doi.org/10.1007/s13226-020-0395-7
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DOI: https://doi.org/10.1007/s13226-020-0395-7