Complex symmetric weighted composition operators on Bergman spaces and Lebesgue spaces

被引：0
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作者：
Pham Viet Hai
Osmar R. Severiano
机构：
[1] Hanoi University of Science and Technology,School of Applied Mathematics and Informatics
[2] Universidade Federal de Campina Grande,Programa Associado de Pós Graduação em Matemática Universidade Federal da Paraíâba
来源：
Analysis and Mathematical Physics | 2022年 / 12卷
关键词：
Weighted composition operator; Complex symmetry; Bergman space; 47B33; 47B32; 47B38; 47B15; 30H20;
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摘要：
In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of conjugations. As it turns out, weighted composition operators enhanced by a symmetry must be bounded. Hermitian, and unitary weighted composition operators are proven to be complex symmetric with respect to an adapted and highly relevant conjugation. We classify which the linear fractional functions give rise to the complex symmetry of bounded composition operators. We end the paper with a natural link to complex symmetry in Lebesgue space.
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