A simple equivalent reformulation of the separable quotient problem (Q343298)
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scientific article; zbMATH DE number 6656737
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A simple equivalent reformulation of the separable quotient problem |
scientific article; zbMATH DE number 6656737 |
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A simple equivalent reformulation of the separable quotient problem (English)
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25 November 2016
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Let \(X\) be a real Banach space. It is not known if there is always a closed subspace \(Y \subset X\) such that the quotient space \(X/Y\) is infinite dimensional and separable. In this short paper, the authors give another equivalent formulation of this problem. \(X\) is said to be hyper-barreled if every closed absolutely convex set whose span is dense in \(X\), has non-empty interior. In terms of this notion the equivalence reads `\(X\) has no infinite-dimensional separable quotient if and only if \(X\) is hyper-barreled.'
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pseudo-barrel
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separable
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quotient
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0.7884994149208069
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0.760149359703064
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