Hilbert-Schmidt differences of composition operators on the Bergman space
- Authors
- Choe, Boo Rim; Hosokawa, Takuya; Koo, Hyungwoon
- Issue Date
- 12월-2011
- Publisher
- SPRINGER
- Keywords
- Composition operator; Hilbert-Schmidt operator; Bergman space; Hilbert-Schmidt norm topology; Unit disk
- Citation
- MATHEMATISCHE ZEITSCHRIFT, v.269, no.3-4, pp.751 - 775
- Indexed
- SCIE
SCOPUS
- Journal Title
- MATHEMATISCHE ZEITSCHRIFT
- Volume
- 269
- Number
- 3-4
- Start Page
- 751
- End Page
- 775
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/111074
- DOI
- 10.1007/s00209-010-0757-7
- ISSN
- 0025-5874
- Abstract
- In the setting of the weighted Bergman space over the unit disk, we characterize Hilbert-Schmidt differences of two composition operators in terms of integrability condition involving pseudohyperbolic distance between the inducing functions. We also show that a linear combination of two composition operators can be Hilbert-Schmidt, except for trivial cases, only when it is essentially a difference. We apply our results to study the topological structure of the space of all composition operators under the Hilbert-Schmidt norm topology. We first characterize components and then provide some sufficient conditions for isolation or for non-isolation.
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