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Complex symmetric weighted composition operators on the Hardy space
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 817-831
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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.
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.
DOI : 10.21136/CMJ.2020.0555-18
Classification : 47B33, 47B38
Keywords: complex symmetry; weighted composition operator; Hardy space 
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Jiang, Cao; Han, Shi-An; Zhou, Ze-Hua. Complex symmetric weighted composition operators on the Hardy space. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 3, pp. 817-831. doi: 10.21136/CMJ.2020.0555-18

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