Commutators and Semi-Commutators of Toeplitz Operators on the Fock Space

In this paper we completely characterize when the commutator and semi-commutator of two monomial-type Toeplitz operators on the Fock space over ℂ n 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-)...

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Bibliographic Details
Published in:Indian journal of pure and applied mathematics 2020-03, Vol.51 (1), p.195-215
Main Author: Dong, Xing-Tang
Format: Article
Language:English
Subjects:
Applications of Mathematics
Commutators
Mathematics
Mathematics and Statistics
Numerical Analysis
Operators
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Summary:In this paper we completely characterize when the commutator and semi-commutator of two monomial-type Toeplitz operators on the Fock space over ℂ n 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.
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-020-0395-7