Bulletin of the Belgian Mathematical Society - Simon Stevin

Adjoint of some composition operators on the Dirichlet and Bergman spaces

A. Abdollahi, S. Mehrangiz, and T. Roientan

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Abstract

Let $\varphi$ be a holomorphic self-map of the unit disk $\mathbb{U}:=\{z\in \mathbb{C}: |z| < 1\}$, and the composition operator with symbol $\varphi$ is defined by $C_\varphi f=f \circ \varphi.$ In this paper we present formula for the adjoint of composition operators in some Hilbert spaces of analytic functions, in the case that $\varphi$ is a finite Blaschke product or a rational univalent holomorphic self-map of the unit disk $\mathbb{U}$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 1 (2015), 59-69.

Dates
First available in Project Euclid: 20 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1426856858

Digital Object Identifier
doi:10.36045/bbms/1426856858

Mathematical Reviews number (MathSciNet)
MR3325721

Zentralblatt MATH identifier
1357.47025

Subjects
Primary: 47B33: Composition operators
Secondary: 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)

Keywords
Dirichlet space composition operator adjoint Blaschke product

Citation

Abdollahi, A.; Mehrangiz, S.; Roientan, T. Adjoint of some composition operators on the Dirichlet and Bergman spaces. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 1, 59--69. doi:10.36045/bbms/1426856858. https://projecteuclid.org/euclid.bbms/1426856858


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