Local dual spaces of a Banach space (Q2759171)
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scientific article; zbMATH DE number 1681004
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Local dual spaces of a Banach space |
scientific article; zbMATH DE number 1681004 |
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Local dual spaces of a Banach space (English)
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11 December 2001
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local dual space
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local reflexivity
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norming subspace
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smallest local dual
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Several characterizations are given of local dual spaces from which many examples are obtained. For instance, if \(\mu\) is a finite positive measure, then \(L_1(\mu,X^*)\) is a local dual of \(L_\infty(\mu,X)\). Every separable space \(X\) has a separable local dual \(Z\) and \(Z\) can be chosen with the metric approximation property if \(X\) has it. Also, a separable space containing no copies of \(\ell_1\) admits a smallest local dual.
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