Strong \(M\)-decompositions in separable Banach spaces (Q1814147)
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scientific article; zbMATH DE number 10194
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Strong \(M\)-decompositions in separable Banach spaces |
scientific article; zbMATH DE number 10194 |
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Strong \(M\)-decompositions in separable Banach spaces (English)
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25 June 1992
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The author proves the following theorem: Let \((p_ n)\) be a sequence of semi-norms on \(E=\ell_ \infty\) which satisfies \(p_ n(x)\to 0\) for each \(x\in E\). Then \(E\) has separable subspaces which do not admit any strong \(M\)-decomposition pointwise bounded by \((p_ n)\). The author takes this theorem as a step towards possible negative solutions of the following problems: (1) Does every separable Banach space have a Schauder decomposition? (2) Does every separable Banach space have a strong \(M\)-basis?
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separable subspaces
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strong \(M\)-decomposition
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separable Banach space
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Schauder decomposition
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strong \(M\)-basis
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