Complex symmetric composition operators on weighted Hardy spaces

 作者： Sivaram K. Narayan,  Daniel Sievewright,  Maria 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 operator;  Conjugation;  Composition operator;  Weighted Hardy space;  Weighted Bergman space;  Linear 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.

• 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