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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-.
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.
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
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