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A simple proof of the Weierstrass-Stone theorem

100%

Zemánek J.

Commentationes Mathematicae

1978

tom 20

nr 2

The article contains no abstract

Precompactness in the uniform ergodic theory

63%

Lyubich Y., Zemánek J.

Studia Mathematica

1994-1995

tom 112

nr 1

89-97

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.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Studia Mathematica

2 Zemánek J.

1 Lyubich Y.

1 1994

1 1978

Wyniki wyszukiwania

A simple proof of the Weierstrass-Stone theorem

Precompactness in the uniform ergodic theory