Geodesic
Precompactness in the uniform ergodic theory
Studia Mathematica, Tome 112 (1994) no. 1, pp. 89-97

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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.
DOI : 10.4064/sm-112-1-89-97

Yu Lyubich 1 ;  1

1 
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Yu Lyubich;  . Precompactness in the uniform ergodic theory. Studia Mathematica, Tome 112 (1994) no. 1, pp. 89-97. doi: 10.4064/sm-112-1-89-97

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