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Spectra of Generalized Cesàro Operators Acting on Growth Spaces

  • Bartosz MalmanEmail author
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Abstract

We study the spectrum of generalized Cesàro operators \(T_g\) acting on the class of growth spaces \(A^{-\alpha }\). We show how the problem of determining the spectrum is related to boundedness of standard weighted Bergman projections on weighted \(L^\infty \)-spaces. Using this relation we establish some general spectral properties of these operators, and explicitly compute the spectrum for a large class of symbols g.

Keywords

Generalized Cesàro operators Volterra-type integral operators Weighted L-infinity spaces Weighted Bergman projections 

Notes

Acknowledgements

The author would like to thank his supervisor, Professor Alexandru Aleman, for the suggestion to study this problem and for many helpful discussions.

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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Centre for Mathematical SciencesLund UniversityLundSweden

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