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3-Complex Symmetric and Complex Normal Weighted Composition Operators on the Weighted Bergman Spaces of the Half-Plane

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  • Zhi-Jie Jiang

    (School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China)

Abstract

One of the aims of this paper is to characterize 3-complex symmetric weighted composition operators induced by three types of symbols on the weighted Bergman space of the right half-plane with the conjugation J f ( z ) = f ( z ¯ ) ¯ . It is well known that the complex symmetry is equivalent to 2-complex symmetry for the weighted composition operators studied in the paper. However, the interesting fact that 3-complex symmetry is not equivalent to 2-complex symmetry for such operators is found in the paper. Finally, the complex normal of such operators on the weighted Bergman space of the right half-plane with the conjugation J is characterized.

Suggested Citation

  • Zhi-Jie Jiang, 2024. "3-Complex Symmetric and Complex Normal Weighted Composition Operators on the Weighted Bergman Spaces of the Half-Plane," Mathematics, MDPI, vol. 12(7), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:980-:d:1363586
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