Weighted Composition Operators on Iterated Weighted-Type Banach Spaces of Analytic Functions

We study a class { V n : n ≥ 0 } of iterated weighted-type Banach spaces of analytic functions on the open unit disk of which the Bloch space and the Zygmund space are special cases. We characterize the bounded and the compact weighted composition operators on V n thereby extending several known res...

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Bibliographic Details
Published in:Complex analysis and operator theory 2019-06, Vol.13 (4), p.1989-2016
Main Authors: Colonna, Flavia, Hmidouch, Nacir
Format: Article
Language:English
Subjects:
Analysis
Analytic functions
Banach spaces
Composition
Mathematical analysis
Mathematics
Mathematics and Statistics
Operator Theory
Operators
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Summary:We study a class { V n : n ≥ 0 } of iterated weighted-type Banach spaces of analytic functions on the open unit disk of which the Bloch space and the Zygmund space are special cases. We characterize the bounded and the compact weighted composition operators on V n thereby extending several known results in the literature. Lastly, we characterize the invertible weighted composition operators on V n and prove that a composition operator on V n is an isometry if and only if its symbol is a rotation.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-019-00905-2