Cancellation properties of composition operators on Bergman spaces

Hyungwoon Koo; Maofa Wang

doi:10.1016/j.jmaa.2015.07.027

Cancellation properties of composition operators on Bergman spaces

Hyungwoon Koo, Maofa Wang

Department of Mathematics

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

10 Citations (Scopus)

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_i are distinct and none of Cϕi is compact, then (C_ϕ1-Cϕ2)-(C_ϕ3-Cϕ1) is compact if and only if both (C_ϕ1-Cϕ2) and (C_ϕ3-Cϕ1) 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	https://doi.org/10.1016/j.jmaa.2015.07.027
Publication status	Published - 2015 Dec 15

Keywords

Compactness
Difference of composition operators
Linear combination

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2015.07.027

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AU - Koo, Hyungwoon

AU - Wang, Maofa

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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

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Cancellation properties of composition operators on Bergman spaces

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Keywords

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