Precompactness in the uniform ergodic theory
Volume 112 / 1994
Studia Mathematica 112 (1994), 89-97
DOI: 10.4064/sm-112-1-89-97
Abstract
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.
