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Composition-differentiation operators on the Hardy space


Authors: Mahsa Fatehi and Christopher N. B. Hammond
Journal: Proc. Amer. Math. Soc. 148 (2020), 2893-2900
MSC (2010): Primary 47B38; Secondary 30H10, 47A05, 47A30, 47B33
DOI: https://doi.org/10.1090/proc/14898
Published electronically: March 18, 2020
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Abstract: Let $ \varphi $ be a nonconstant analytic self-map of the open unit disk in $ \mathbb{C}$, with $ \Vert\varphi \Vert _{\infty }<1$. Consider the operator $ D_{\varphi }$, acting on the Hardy space $ H^{2}$, given by differentiation followed by composition with $ \varphi $. We obtain results relating to the adjoint, norm, and spectrum of such an operator.


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Additional Information

Mahsa Fatehi
Affiliation: Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran
Email: fatehimahsa@yahoo.com

Christopher N. B. Hammond
Affiliation: Department of Mathematics and Statistics, Connecticut College, New London, Connecticut 06320
Email: cnham@conncoll.edu

DOI: https://doi.org/10.1090/proc/14898
Received by editor(s): August 2, 2019
Published electronically: March 18, 2020
Communicated by: Stephan Ramon Garcia
Article copyright: © Copyright 2020 American Mathematical Society