Abstract
Let E be a complex Banach space with open unit ball \(B_E.\) For analytic self-maps \(\varphi \) of \(B_E\) with \(\varphi (0) =0,\) we investigate the spectra of weighted composition operators \(uC_\varphi \) acting on a large class of spaces of analytic functions. This class contains, for example, weighted Banach spaces of \(H^\infty \)-type on \(B_E\), weighted Bergman spaces \(A^p_\alpha ({\mathbb {B}}_N)\) and Hardy spaces \(H^p({\mathbb {B}}_N).\) We present a general approach for deducing new information about the spectrum and for estimating the essential spectral radius of \(uC_\varphi .\)
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Acknowledgements
The research in this paper was initiated during a visit of Pablo Galindo to Ȧbo Akademi University. He thankfully acknowledges Mikael Lindström’s friendly hospitality.
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Pablo Galindo was partially supported by Spanish MINECO/FEDER PGC2018-094431-B-I00. Mikael Lindström was partially supported by MTM2014-53241-P and the Academy of Finland project 296718.
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Galindo, P., Lindström, M. & Wikman, N. Spectra of Weighted Composition Operators on Analytic Function Spaces. Mediterr. J. Math. 17, 34 (2020). https://doi.org/10.1007/s00009-019-1465-0
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DOI: https://doi.org/10.1007/s00009-019-1465-0