An example of an asymptotically Hilbertian space which fails the approximation property (Q2723500)
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scientific article; zbMATH DE number 1614770
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An example of an asymptotically Hilbertian space which fails the approximation property |
scientific article; zbMATH DE number 1614770 |
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An example of an asymptotically Hilbertian space which fails the approximation property (English)
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5 July 2001
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approximation property
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weak Hilbert space
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unconditional basis
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asymptotically Hilbertian property
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A Banach space \(E\) is constructed which is asymptotically Hilbertian and fails the approximation property. This object appears as a subspace of an unconditional basis space \(Z\) fulfilling NEWLINENEWLINENEWLINE(i) \(Z\) is ``almost'' a weak Hilbert space and NEWLINENEWLINENEWLINE(ii) \(Z\) may be written as the direct sum \(Z_1\oplus Z_2\), where all subspaces of these factors have the approximation property.
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