Ergodic Type Theorems via Statistical Convergence

Abstract

In the present paper we obtain some mean ergodic and uniform ergodic type theorems via statistical convergence in a Banach space. We prove, in this case that, the mean ergodic decomposition remains true. We also characterize statistical uniformly ergodicity for an operator $T\in B(X)$ under the condition $st-\lim\limits_{n}\dfrac{\|T^{n}\|}{n}=0$.