Ranks of commutators of Toeplitz operators on the harmonic Bergman space

Yong Chen; Hyungwoon Koo; Young Joo Lee

doi:10.1007/s00020-012-2020-6

Ranks of commutators of Toeplitz operators on the harmonic Bergman space

Yong Chen, Hyungwoon Koo, Young Joo Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We study the rank of commutators of two Toeplitz operators on the harmonic Bergman space of the unit disk. We first show that the commutator of any two Toeplitz operators with general symbols can't have an odd rank. But, given any integer n ≥ 0, we also show that there are two symbols for which the corresponding Toeplitz operators induce the commutator with rank 2n exactly.

Original language	English
Pages (from-to)	31-38
Number of pages	8
Journal	Integral Equations and Operator Theory
Volume	75
Issue number	1
DOIs	https://doi.org/10.1007/s00020-012-2020-6
Publication status	Published - 2013 Jan

Keywords

Toeplitz operator
finite rank
harmonic Bergman space

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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abstract = "We study the rank of commutators of two Toeplitz operators on the harmonic Bergman space of the unit disk. We first show that the commutator of any two Toeplitz operators with general symbols can't have an odd rank. But, given any integer n ≥ 0, we also show that there are two symbols for which the corresponding Toeplitz operators induce the commutator with rank 2n exactly.",

keywords = "Toeplitz operator, finite rank, harmonic Bergman space",

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AB - We study the rank of commutators of two Toeplitz operators on the harmonic Bergman space of the unit disk. We first show that the commutator of any two Toeplitz operators with general symbols can't have an odd rank. But, given any integer n ≥ 0, we also show that there are two symbols for which the corresponding Toeplitz operators induce the commutator with rank 2n exactly.

KW - Toeplitz operator

KW - finite rank

KW - harmonic Bergman space

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