Complex symmetric composition operators on weighted Hardy spaces
作者: Sivaram K. NarayanDaniel SievewrightMaria Tjani
刊名: Proceedings of the American Mathematical Society, 2020, Vol.148 (5), pp.2117-2127
来源数据库: American Mathematical Society Journal
DOI: 10.1090/proc/14909
关键词: Complex symmetric operatorConjugationComposition operatorWeighted Hardy spaceWeighted Bergman spaceLinear fractional maps.
原始语种摘要: Let $ \varphi $ be an analytic self-map of the open unit disk $ \mathbb{D}$. We study the complex symmetry of composition operators $ C_\varphi $ on weighted Hardy spaces induced by a bounded sequence. For any analytic self-map of $ \mathbb{D}$ that is not an elliptic automorphism, we establish that if $ C_{\varphi }$ is complex symmetric, then either $ \varphi (0)=0$ or $ \varphi $ is linear. In the case of weighted Bergman spaces $ A^{2}_{\alpha }$, we find the non-automorphic linear fractional symbols $ \varphi $ such that $ C_{\varphi }$ is complex symmetric.
全文获取路径: AMS 

  • symmetric 对称的
  • operators 操作符
  • weighted 加权
  • fractional 分级的
  • automorphic 自形的
  • automorphism 自同构
  • complex 超群
  • analytic 解析的
  • bounded 有界的
  • symmetry 对称