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Title: Compact and Hilbert-Schmidt weighted composition operators on weighted Bergman spaces
Authors: Lo, CO 
Loh, AWK 
Issue Date: Oct-2022
Source: Journal of the australian mathematical society, Oct. 2022, v. 113, no. 2, p. 208-225
Abstract: Let u and φ be two analytic functions on the unit disk D such that φ(D)⊂D . A weighted composition operator uCφ induced by u and φ is defined on A2α , the weighted Bergman space of D, by uCφf:=u⋅f∘φ for every f∈A2α . We obtain sufficient conditions for the compactness of uCφ in terms of function-theoretic properties of u and φ . We also characterize when uCφ on A2α is Hilbert–Schmidt. In particular, the characterization is independent of α when φ is an automorphism of D. Furthermore, we investigate the Hilbert–Schmidt difference of two weighted composition operators on A2α.
Keywords: Weighted composition operators
Weighted Bergman spaces
Compact operators
Hilbert-Schmidt operators
Publisher: Cambridge University Press
Journal: Journal of the australian mathematical society 
ISSN: 1446-7887
EISSN: 1446-8107
DOI: 10.1017/S1446788722000039
Rights: © The Author(s), 2021. Published by Cambridge University Press on behalf of The Nutrition Society. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
The following publication Lo, C., & Loh, A. (2022). Compact and Hilbert-Schmidt weighted composition operators on weighted Bergman spaces. Journal of the Australian Mathematical Society, 113(2), 208-225 is available at https://doi.org/10.1017/S1446788722000039.
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