UNIFORM AND STRONG ERGODIC THEOREMS IN BANACH SPACES

摘要

In his study of the spectral theory of bounded linear operators on a Banach space, N. Dunford gave some necessary and sufficient conditions for the convergence in various topologies of a sequence of operator functions to a projection and established a systematic theory of uniform and strong (i.e., mean) ergodic theorems in Banach spaces. But the equivalence of Cesaro, Hausdorff, and Abel summability of a sequence of operators had not yet been considered in the concrete.