Annals of Functional Analysis

Adjoints of generalized composition operators with rational symbol

Aliakbar Salaryan and Hamid Vaezi

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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

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

First available in Project Euclid: 1 July 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

generalized composition operator adjoint reproducing kernel weighted Hardy space


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.

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