Annals of Functional Analysis

Adjoints of generalized composition operators with rational symbol

Aliakbar Salaryan and Hamid Vaezi

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Abstract

Given $\varphi:\mathbb{U}\rightarrow\mathbb{U}$, an analytic self-map of the open unit disc in complex plane, the composition operator $C_{\varphi}$ is defined by $C_{\varphi}f=f\circ\varphi$ for $f$ belonging to some Hilbert space of analytic functions on $\mathbb{U}$. In the present paper, we introduce a generalization of the composition operators and reproducing kernel functions on the weighted Hardy spaces. We also obtain the adjoints of generalized composition operators with rational symbol acting on the Hardy, Bergman and Dirichlet spaces.

Article information

Source
Ann. Funct. Anal., Volume 6, Number 4 (2015), 215-225.

Dates
First available in Project Euclid: 1 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.afa/1435764013

Digital Object Identifier
doi:10.15352/afa/06-4-215

Mathematical Reviews number (MathSciNet)
MR3365993

Zentralblatt MATH identifier
1323.47032

Subjects
Primary: 47B33: Composition operators
Secondary: 47B38: Operators on function spaces (general) 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)

Keywords
generalized composition operator adjoint reproducing kernel weighted Hardy space

Citation

Salaryan, Aliakbar; Vaezi, Hamid. Adjoints of generalized composition operators with rational symbol. Ann. Funct. Anal. 6 (2015), no. 4, 215--225. doi:10.15352/afa/06-4-215. https://projecteuclid.org/euclid.afa/1435764013


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