Complex symmetric weighted composition operators on Dirichlet spaces and Hardy spaces in the unit ball

2018/12/26 by Xiaohe Hu, Hu, Xiao-He, Zicong Yang +3
Mathematics · #32A35 #32A37 #47B15 #47B33 #47B38 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1812.10248

openalex publication_date 2018/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate when weighted composition operators acting on Dirichlet spaces D(\mathbbB_N) are complex symmetric with respect to some special conjugations, and provide some characterizations of Hermitian weighted composition operators on D(\mathbbB_N). Furthermore, we give a sufficient and necessary condition for J-symmetric weighted composition operators on Hardy spaces H²(\mathbbB_N) to be unitary or Hermitian, then some new examples of complex symmetric weighted composition operators on H²(\mathbbB_N) are obtained. We also discuss the normality of complex symmetric weighted composition operators on H²(\mathbbB_N).

Related

• Generalized weighted composition operators on weighted Hardy spaces
• A note on the complex symmetric weighted composition operators over Hardy space
• Normal complex symmetric weighted composition operators on the Hardy space
• Complex symmetric weighted composition operators on Bergman spaces and Lebesgue spaces
• Operators commuting with complex symmetric weighted composition operators on H²