# Precompactness in the uniform ergodic theory

Studia Mathematica (1994)

- Volume: 112, Issue: 1, page 89-97
- ISSN: 0039-3223

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topLyubich, Yu., and Zemánek, J.. "Precompactness in the uniform ergodic theory." Studia Mathematica 112.1 (1994): 89-97. <http://eudml.org/doc/216140>.

@article{Lyubich1994,

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.},

author = {Lyubich, Yu., Zemánek, J.},

journal = {Studia Mathematica},

keywords = {Banach space operators; arithmetic means; precompact set in the operator norm topology},

language = {eng},

number = {1},

pages = {89-97},

title = {Precompactness in the uniform ergodic theory},

url = {http://eudml.org/doc/216140},

volume = {112},

year = {1994},

}

TY - JOUR

AU - Lyubich, Yu.

AU - Zemánek, J.

TI - Precompactness in the uniform ergodic theory

JO - Studia Mathematica

PY - 1994

VL - 112

IS - 1

SP - 89

EP - 97

AB - 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.

LA - eng

KW - Banach space operators; arithmetic means; precompact set in the operator norm topology

UR - http://eudml.org/doc/216140

ER -

## References

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