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 | |
| Publication status | Published - 2013 Jan 1 |
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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 journal › Article
}
TY - JOUR
T1 - Ranks of commutators of Toeplitz operators on the harmonic Bergman space
AU - Chen, Yong
AU - Koo, Hyung Woon
AU - Lee, Young Joo
PY - 2013/1/1
Y1 - 2013/1/1
N2 - 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.
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 - finite rank
KW - harmonic Bergman space
KW - Toeplitz operator
UR - http://www.scopus.com/inward/record.url?scp=84871934652&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84871934652&partnerID=8YFLogxK
U2 - 10.1007/s00020-012-2020-6
DO - 10.1007/s00020-012-2020-6
M3 - Article
AN - SCOPUS:84871934652
VL - 75
SP - 31
EP - 38
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 1
ER -