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Weighted composition operators on Korenblum type spaces of analytic functions

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

We investigate the continuity, compactness and invertibility of weighted composition operators \(W_{\psi ,\varphi }{:}\, f \rightarrow \psi (f \circ \varphi )\) when they act on the classical Korenblum space \(A^{-\infty }\) and other related Fréchet or (LB)-spaces of analytic functions on the open unit disc which are defined as intersections or unions of weighted Banach spaces with sup-norms. Some results about the spectrum of these operators are presented in case the self-map \(\varphi \) has a fixed point in the unit disc. A precise description of the spectrum is obtained in this case when the operator acts on the Korenblum space.

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Acknowledgements

This paper is part of the PhD thesis of the author, which is supervised by J. Bonet and P. Galindo. The author is thankful to them for their guidance and helpful suggestions. She also thanks the referees for the very careful reading of the manuscript.

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Correspondence to Esther Gómez-Orts.

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This research was partially supported by the research project MTM2016-76647-P and the grant BES-2017-081200.

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Gómez-Orts, E. Weighted composition operators on Korenblum type spaces of analytic functions. RACSAM 114, 199 (2020). https://doi.org/10.1007/s13398-020-00924-1

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