Ranks of commutators of Toeplitz operators on the harmonic Bergman space

Yong Chen, Hyung Woon Koo, Young Joo Lee

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)31-38
Number of pages8
JournalIntegral Equations and Operator Theory
Volume75
Issue number1
DOIs
Publication statusPublished - 2013 Jan 1

Fingerprint

Harmonic Bergman Space
Toeplitz Operator
Commutator
Unit Disk
Odd
Integer

Keywords

  • finite rank
  • harmonic Bergman space
  • Toeplitz operator

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis

Cite this

Ranks of commutators of Toeplitz operators on the harmonic Bergman space. / Chen, Yong; Koo, Hyung Woon; Lee, Young Joo.

In: Integral Equations and Operator Theory, Vol. 75, No. 1, 01.01.2013, p. 31-38.

Research output: Contribution to journalArticle

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