Abstract
Introduction. The purpose of this paper is to extend various known results in operator ergodic theory to give a direct approach to pointwise ergodic theorems. The main step in this approach is a maximal ergodic theorem (Theorem 1), which is a generalization of the result given in [1]. A corollary (Theorem 2) of this theorem is Chacon's ergodic theorem [6] for positive operators which contains both Birkhoff's ergodic theorem [2] (or, more generally, Dunford-Schwartz's theorem [9] for positive contractions) and Chacon-Ornstein's ratio ergodic theorem [4]. Theorem 1 is also used to obtain the identification of the limit in a straightforward way. In the final part of the paper Theorem 2 is generalized to nonpositive operators to give a direct proof of Chacon's general ergodic theorem [6].
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