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On ergodic theorem for a family of operators. (English) Zbl 1497.37005

Summary: In this paper, we obtain a generalization of the uniform ergodic theorem to the family of bounded linear operators on a Banach space. We present some elementary results in this setting and we show that Lin’s theorem can be extended from the case of a bounded linear operator to the case of a family of bounded linear operators acting on a Banach space.

MSC:

37A30 Ergodic theorems, spectral theory, Markov operators
47A35 Ergodic theory of linear operators
47B40 Spectral operators, decomposable operators, well-bounded operators, etc.
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