The Cesàro operator on power series spaces

[EN] The discrete Cesaro operator C is investigated in the class of power series spaces Lambda(0) (alpha) of finite type. Of main interest is its spectrum, which is distinctly different in the cases when Lambda(0) (alpha) is nuclear and when it is not. Actually, the nuclearity of Lambda(0) (alpha) is characterized via certain properties of the spectrum of C. Moreover, C is always power bounded, uniformly mean ergodic, and whenever Lambda(0) (alpha) is nuclear, also (I - C)(m) (Lambda(0) (alpha)) is closed in Lambda(0) (alpha) for each m is an element of N.The research of the first two authors was partially supported by the projects MTM2013-43540-P, MTM2016-76647-P and GVA Prometeo II/2013/013.Albanese, A.; Bonet Solves, JA.; Ricker, WJ. (2018). The Cesàro operator on power series spaces. Studia Mathematica. 240(1):47-68. doi:10.4064/sm8590-2-2017S4768240