The Cesàro operator on Korenblum type spaces of analytic functions

[EN] The spectrum of the CesA ro operator , which is always continuous (but never compact) when acting on the classical Korenblum space and other related weighted Fr,chet or (LB) spaces of analytic functions on the open unit disc, is completely determined. It turns out that such spaces are always Schwartz but, with the exception of the Korenblum space, never nuclear. Some consequences concerning the mean ergodicity of are deduced.The research of the first two authors was partially supported by the projects MTM2013-43540-P and MTM2016-76647-P. The second author gratefully acknowledges the support of the Alexander von Humboldt Foundation.Albanese, A.; Bonet Solves, JA.; Ricker, WJ. (2018). The Cesàro operator on Korenblum type spaces of analytic functions. Collectanea mathematica. 69(2):263-281. https://doi.org/10.1007/s13348-017-0205-7263281692Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. 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