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

Zhi-Jie Jiang ()
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Zhi-Jie Jiang: School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China

Mathematics, 2024, vol. 12, issue 7, 1-12

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.

Keywords: weighted Bergman space; weighted composition operator; 3-complex symmetric operator; complex normal operator; right half-plane (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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