@article{Tajmouati_El Bakkali_Barki_2019, title={On the uniform ergodic theorem in invariant subspaces.}, volume={38}, url={https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3578}, abstractNote={Let T be a bounded linear operator on a Banach space X into itself. In this paper, we study the uniform ergodicity of the operator T|Y when Y is a closed subspace invariant under T. We show that if T satisfies, lim n →∞ || T n ||/ n = 0 ,then T is uniformly ergodic on X if and only if the restriction of T to some closed subspace Y ⊂ X, invariant under T and R[(I − T)k] ⊂ Y for some integer k ≥ 1, is uniformly ergodic. Consequently, we obtain other equivalent conditions concerning the theorem of Mbekhta and Zemànek ((9), theorem 1), also to the theorem of the Gelfand-Hille type.}, number={2}, journal={Proyecciones (Antofagasta, On line)}, author={Tajmouati, Abdelaziz and El Bakkali, Abdeslam and Barki, Fatih}, year={2019}, month={May}, pages={315-324} }