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.References
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Additional Information
- Sivaram K. Narayan
- Affiliation: Department of Mathematics, Central Michigan University, Mt. Pleasant, Michigan 48859
- MR Author ID: 314357
- Email: sivaram.narayan@cmich.edu
- Daniel Sievewright
- Affiliation: 5235 S. Chandler Rd., St. Johns, Michigan 48879
- MR Author ID: 1106238
- Email: dssievewright@gmail.com
- Maria Tjani
- Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
- MR Author ID: 666446
- Email: mtjani@uark.edu
- Received by editor(s): July 26, 2019
- Received by editor(s) in revised form: September 30, 2019
- Published electronically: February 12, 2020
- Communicated by: Stephan Ramon Garcia
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 2117-2127
- MSC (2010): Primary 47B33, 47B32, 47B99
- DOI: https://doi.org/10.1090/proc/14909
- MathSciNet review: 4078096