Abstract
The compact difference of two composition operators on the Bergman spaces over the unit disc is characterized in [11] in terms of certain cancellation property of the inducing maps at every "bad" boundary points, which make each single composition operator not to be compact. In this paper, we completely characterize the compactness of a linear combination of three composition operators on the Bergman space. As one consequence of this characterization, we show that there is no cancellation property for the compactness of double difference of composition operators. More precisely, we show that if ϕ<inf>i</inf> are distinct and none of Cϕi is compact, then (C<inf>ϕ1-Cϕ2</inf>)-(C<inf>ϕ3-Cϕ1</inf>) is compact if and only if both (C<inf>ϕ1-Cϕ2</inf>) and (C<inf>ϕ3-Cϕ1</inf>) are compact.
| Original language | English |
|---|---|
| Pages (from-to) | 1174-1182 |
| Number of pages | 9 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 432 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2015 Dec 15 |
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Keywords
- Compactness
- Difference of composition operators
- Linear combination
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
Cancellation properties of composition operators on Bergman spaces. / Koo, Hyung Woon; Wang, Maofa.
In: Journal of Mathematical Analysis and Applications, Vol. 432, No. 2, 15.12.2015, p. 1174-1182.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Cancellation properties of composition operators on Bergman spaces
AU - Koo, Hyung Woon
AU - Wang, Maofa
PY - 2015/12/15
Y1 - 2015/12/15
N2 - The compact difference of two composition operators on the Bergman spaces over the unit disc is characterized in [11] in terms of certain cancellation property of the inducing maps at every "bad" boundary points, which make each single composition operator not to be compact. In this paper, we completely characterize the compactness of a linear combination of three composition operators on the Bergman space. As one consequence of this characterization, we show that there is no cancellation property for the compactness of double difference of composition operators. More precisely, we show that if ϕi are distinct and none of Cϕi is compact, then (Cϕ1-Cϕ2)-(Cϕ3-Cϕ1) is compact if and only if both (Cϕ1-Cϕ2) and (Cϕ3-Cϕ1) are compact.
AB - The compact difference of two composition operators on the Bergman spaces over the unit disc is characterized in [11] in terms of certain cancellation property of the inducing maps at every "bad" boundary points, which make each single composition operator not to be compact. In this paper, we completely characterize the compactness of a linear combination of three composition operators on the Bergman space. As one consequence of this characterization, we show that there is no cancellation property for the compactness of double difference of composition operators. More precisely, we show that if ϕi are distinct and none of Cϕi is compact, then (Cϕ1-Cϕ2)-(Cϕ3-Cϕ1) is compact if and only if both (Cϕ1-Cϕ2) and (Cϕ3-Cϕ1) are compact.
KW - Compactness
KW - Difference of composition operators
KW - Linear combination
UR - http://www.scopus.com/inward/record.url?scp=84939257434&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84939257434&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2015.07.027
DO - 10.1016/j.jmaa.2015.07.027
M3 - Article
AN - SCOPUS:84939257434
VL - 432
SP - 1174
EP - 1182
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 2
ER -