TY - JOUR AU - Tajmouati, Abdelaziz AU - El Bakkali, Abdeslam AU - Barki, Fatih PY - 2019/05/31 Y2 - 2024/03/28 TI - On the uniform ergodic theorem in invariant subspaces. JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 38 IS - 2 SE - DO - UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3578 SP - 315-324 AB - 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. ER -