A simple proof of the Weierstrass-Stone theorem
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On Uniform Continuity of the Spectral Radius in Banach Algebras.
Precompactness in the uniform ergodic theory
We characterize the Banach space operators T whose arithmetic means form a precompact set in the operator norm topology. This occurs if and only if the sequence 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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