Complex symmetric composition operators on weighted Hardy spaces

Narayan, Sivaram; Sievewright, Daniel; Tjani, Maria

doi:10.1090/proc/14909

Complex symmetric composition operators on weighted Hardy spaces
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by Sivaram K. Narayan, Daniel Sievewright and Maria Tjani PDF

Proc. Amer. Math. Soc. 148 (2020), 2117-2127 Request permission

Abstract:

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.

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