2021/05/31 by Pham Viet Hai, Hai, Pham Viet, Osmar R. Severiano +1 · 1 citation
Mathematics · #30H20 #47B15 #47B32 #47B33 #47B38 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2105.14979
openalex publication_date 2021/05/31 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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.