## Compositionâdifferentiation operators on the Hardy space

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- by Mahsa Fatehi and Christopher N. B. Hammond PDF
- Proc. Amer. Math. Soc.
**148**(2020), 2893-2900 Request permission

## Abstract:

Let $\varphi$ be a nonconstant analytic self-map of the open unit disk in $\mathbb {C}$, with $\|\varphi \|_{\infty }<1$. 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.## References

- Carl C. Cowen,
*Linear fractional composition operators on $H^2$*, Integral Equations Operator Theory**11**(1988), no.Â 2, 151â160. MR**928479**, DOI 10.1007/BF01272115 - Carl C. Cowen and Barbara D. MacCluer,
*Composition operators on spaces of analytic functions*, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995. MR**1397026** - Domingo A. Herrero,
*The Volterra operator is a compact universal quasinilpotent*, Integral Equations Operator Theory**1**(1978), no.Â 4, 580â588. MR**516769**, DOI 10.1007/BF01682942 - R. A. Hibschweiler and N. Portnoy,
*Composition followed by differentiation between Bergman and Hardy spaces*, Rocky Mountain J. Math.**35**(2005), no.Â 3, 843â855. MR**2150311**, DOI 10.1216/rmjm/1181069709 - ShĂ»ichi Ohno,
*Products of composition and differentiation between Hardy spaces*, Bull. Austral. Math. Soc.**73**(2006), no.Â 2, 235â243. MR**2217942**, DOI 10.1017/S0004972700038818 - Dragan VukotiÄ,
*Analytic Toeplitz operators on the Hardy space $H^p$: a survey*, Bull. Belg. Math. Soc. Simon Stevin**10**(2003), no.Â 1, 101â113. MR**2032329**

## Additional Information

**Mahsa Fatehi**- Affiliation: Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran
- MR Author ID: 892247
- Email: fatehimahsa@yahoo.com
**Christopher N. B. Hammond**- Affiliation: Department of Mathematics and Statistics, Connecticut College, New London, Connecticut 06320
- MR Author ID: 728945
- Email: cnham@conncoll.edu
- Received by editor(s): August 2, 2019
- Published electronically: March 18, 2020
- Communicated by: Stephan Ramon Garcia
- © Copyright 2020 American Mathematical Society
- 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
- MathSciNet review: 4099777