Non-archimedean Eberlein-Šmulian theory (Q1922839)
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scientific article; zbMATH DE number 930039
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-archimedean Eberlein-Šmulian theory |
scientific article; zbMATH DE number 930039 |
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Non-archimedean Eberlein-Šmulian theory (English)
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30 September 1996
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Summary: It is shown that, for a large class of non-Archimedean normed spaces \(E\), a subset \(X\) is weakly compact as soon as \(f(X)\) is compact for all \(f\in E'\), a fact that has no analogue in functional analysis over the real or complex numbers. As a corollary, we derive a non-Archimedean version of the Eberlein-Šmulian Theorem.
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non-Archimedean normed spaces
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weakly compact
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Eberlein-Šmulian Theorem
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0.8759411
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