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|Title:||Path components of the space of (weighted) composition operators on Bergman spaces||Authors:||Abanin, Alexander V.
Khoi, Le Hai
Tien, Pham Trong
|Keywords:||Science::Mathematics||Issue Date:||2021||Source:||Abanin, A. V., Khoi, L. H. & Tien, P. T. (2021). Path components of the space of (weighted) composition operators on Bergman spaces. Integral Equations and Operator Theory, 93(1), 5-. https://dx.doi.org/10.1007/s00020-020-02615-3||Journal:||Integral Equations and Operator Theory||Abstract:||The topological structure of the set of (weighted) composition operators has been studied on various function spaces on the unit disc such as Hardy spaces, the space of bounded holomorphic functions, weighted Banach spaces of holomorphic functions with sup-norm, Hilbert Bergman spaces. In this paper we consider this problem for all Bergman spaces Aαp with p∈ (0 , ∞) and α∈ (- 1 , ∞). In this setting we establish a criterion for two composition operators to be linearly connected in the space of composition operators; furthermore, for the space of weighted composition operators, we prove that the set of compact weighted composition operators is path connected, but it is not a component.||URI:||https://hdl.handle.net/10356/159740||ISSN:||0378-620X||DOI:||10.1007/s00020-020-02615-3||Schools:||School of Physical and Mathematical Sciences||Rights:||© 2021 Springer Nature Switzerland AG. All rights reserved.||Fulltext Permission:||none||Fulltext Availability:||No Fulltext|
|Appears in Collections:||SPMS Journal Articles|
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