Czechoslovak Mathematical Journal, first online, pp. 1-15


Complex symmetric weighted composition operators on the Hardy space

Cao Jiang, Shi-An Han, Ze-Hua Zhou

Received December 18, 2018.   Published online March 23, 2020.

Abstract:  This paper identifies a class of complex symmetric weighted composition operators on $H^2(\mathbb{D})$ that includes both the unitary and the Hermitian weighted composition operators, as well as a class of normal weighted composition operators identified by Bourdon and Narayan. A characterization of algebraic weighted composition operators with degree no more than two is provided to illustrate that the weight function of a complex symmetric weighted composition operator is not necessarily linear fractional.
Keywords:  complex symmetry; weighted composition operator; Hardy space
Classification MSC:  47B33, 47B38
DOI:  10.21136/CMJ.2020.0555-18

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Affiliations:   Cao Jiang, School of Mathematics and Information Sciences, Nanchang Hangkong University, 696 Fenghe South Avenue, Nanchang 330063, P. R. China, e-mail: jiangcc96@163.com; Shi-An Han, College of Science, Civil Aviation University of China, 2898 Jinbei Highway, Dongli, Tianjin 300300, P. R. China, e-mail: hsatju@163.com; Ze-Hua Zhou (corresponding author), School of Mathematics, Tianjin University, 135 Yaguan Road, Haihe Education Park, Jinnan, Tianjin 300350, P. R. China, e-mail: zehuazhoumath@aliyun.com, zhzhou@tju.edu.cn


 
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