Uniform monotonicity of norms and the strong ``zero-two'' law (Q1263804)
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scientific article; zbMATH DE number 4127929
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniform monotonicity of norms and the strong ``zero-two'' law |
scientific article; zbMATH DE number 4127929 |
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Uniform monotonicity of norms and the strong ``zero-two'' law (English)
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1989
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Extending previous results of Ornstein-Sucheston, Katznelson-Tzafriri and Wittmann the author proves the following theorem. Let E be a Banach lattice having uniformly monotone norm and let T be a positive contraction on E. If \(\| | T^{k+1}-T^ k| \| <0\) for some \(k\in {\mathbb{N}}\), then \(\lim_{n\to \infty}\| | T^{n+1}-T^ n| \| =0.\)
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Banach lattice
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uniformly monotone norm
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positive contraction
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