Abstract
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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Acknowledgements
The paper was completed during a scientific stay of P.V. Hai at the Vietnam Institute for Advanced Study in Mathematics (VIASM), whose hospitality is gratefully appreciated. O.R. Severiano is a postdoctoral fellowship at Programa Associado de Pós Graduação em Matemática UFPB/UFCG, and is supported by INCTMat Grant 88887.613486/2021-00.
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Hai, P.V., Severiano, O.R. Complex symmetric weighted composition operators on Bergman spaces and Lebesgue spaces. Anal.Math.Phys. 12, 43 (2022). https://doi.org/10.1007/s13324-022-00651-3
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DOI: https://doi.org/10.1007/s13324-022-00651-3