Complex symmetric difference of the weighted composition operators on weighted Bergman space of the half-plane

The main goal of this paper was to completely characterize complex symmetric difference of the weighted composition operators induced by three type symbols on weighted Bergman space of the right half-plane with the conjugations $ \mathcal{J}f(z) = \overline{f(\bar{z})} $, $ \mathcal{J}_sf(z) = \over...

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Published inAIMS mathematics Vol. 9; no. 3; pp. 7253 - 7272
Main Author Jiang, Zhi-jie
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
complex symmetric difference of operators
reproducing kernel
weighted bergman space of the right half-plane
weighted composition operator
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Abstract The main goal of this paper was to completely characterize complex symmetric difference of the weighted composition operators induced by three type symbols on weighted Bergman space of the right half-plane with the conjugations $ \mathcal{J}f(z) = \overline{f(\bar{z})} $, $ \mathcal{J}_sf(z) = \overline{f(\bar{z}+is)} $, and $ \mathcal{J}_*f(z) = \frac{1}{z^{{\alpha}+2}}\overline{f(\frac{1}{\bar{z}})} $. The special phenomenon that we focus on is that the difference is complex symmetric on weighted Bergman spaces of the half-plane with the related conjugation if and only if each weighted composition operator is complex symmetric.
AbstractList The main goal of this paper was to completely characterize complex symmetric difference of the weighted composition operators induced by three type symbols on weighted Bergman space of the right half-plane with the conjugations $ \mathcal{J}f(z) = \overline{f(\bar{z})} $, $ \mathcal{J}_sf(z) = \overline{f(\bar{z}+is)} $, and $ \mathcal{J}_*f(z) = \frac{1}{z^{{\alpha}+2}}\overline{f(\frac{1}{\bar{z}})} $. The special phenomenon that we focus on is that the difference is complex symmetric on weighted Bergman spaces of the half-plane with the related conjugation if and only if each weighted composition operator is complex symmetric.
Author Jiang, Zhi-jie
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  organization: School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, China, South Sichuan Center for Applied Mathematics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, China
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SubjectTerms complex symmetric difference of operators
reproducing kernel
weighted bergman space of the right half-plane
weighted composition operator
Title Complex symmetric difference of the weighted composition operators on weighted Bergman space of the half-plane
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