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Precompactness in the uniform ergodic theory

Yu. Lyubich, J. Zemánek (1994)

Studia Mathematica

We characterize the Banach space operators T whose arithmetic means n - 1 ( I + T + . . . + T n - 1 ) n ≥ 1 form a precompact set in the operator norm topology. This occurs if and only if the sequence n - 1 T n n ≥ 1 is precompact and the point 1 is at most a simple pole of the resolvent of T. Equivalent geometric conditions are also obtained.

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