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Compact linear combination of composition operators on Bergman spaces
- Authors
- Choe, Boo Rim; Koo, Hyungwoon; Wang, Maofa
- Issue Date
- 15-3월-2020
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Composition operator; Compact operator; Linear combination; Weighted Bergman space
- Citation
- JOURNAL OF FUNCTIONAL ANALYSIS, v.278, no.5
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF FUNCTIONAL ANALYSIS
- Volume
- 278
- Number
- 5
- ISSN
- 0022-1236
- Abstract
- Motivated by the question of Shapiro and Sundberg raised in 1990, study on linear combinations of composition operators has been a topic of growing interest. In this paper, we completely characterize the compactness of any finite linear combination of composition operators with general symbols on the weighted Bergman spaces in two classical terms: one is a function theoretic characterization of Julia-Caratheodory type and the other is a measure theoretic characterization of Carleson type. Our approach is completely different from what has been known so far. (C) 2019 Elsevier Inc. All rights reserved.
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