The Cesàro operator on weighted l_1 spaces

This is the peer reviewed version of the following article: Albanese, Angela, Bonet Solves, José Antonio, Ricker, W.. (2018). The Cesàro operator on weighted l_1 spaces.Mathematische Nachrichten, 291, 7, 1015-1048, which has been published in final form at http://doi.org/10.1002/mana.201600509. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.[EN] Unlike for l(p), 1 < p <= infinity, the discrete Cesaro operator C does not map l(1) into itself. We identify precisely those weights w such that C does map l(1)(w) continuously into itself. For these weights a complete description of the eigenvalues and the spectrum of C are presented. It is also possible to identify all w such that C is a compact operator in l(1)(w). The final section investigates the mean ergodic properties of C in l(1)(w). Many examples are presented in order to supplement the results and to illustrate the phenomena that occur.Ministry of Education, Science and Art, Bavaria (Germany); Grant: International Visiting Professor Program 2016; Ministry of Economy of Spain; Grant: projects MTM2013-43540-P and MTM2016-76647-PAlbanese, A.; Bonet Solves, JA.; Ricker, W. (2018). The Cesàro operator on weighted l_1 spaces. Mathematische Nachrichten. 291(7):1015-1048. https://doi.org/10.1002/mana.20160050910151048291