Ultrafilters over \(N\) and operators on \(L^ 1\) (Q1815511)
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scientific article; zbMATH DE number 944414
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Ultrafilters over \(N\) and operators on \(L^ 1\) |
scientific article; zbMATH DE number 944414 |
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Ultrafilters over \(N\) and operators on \(L^ 1\) (English)
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12 November 1996
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The author shows that, if the Banach space \(X\) fails the CCP (not every operator from \(L^1\) into \(X\) is Dunford-Pettis) then there exists a subspace \(Z\) of \(X\) which has a finite-dimensional decomposition and contains a \(\delta\)-tree which is in addition a \(\delta\)-Rademacher tree. (Hence, in particular, \(Z\) also fails the CCP).
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Rademacher tree
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CCP
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Dunford-Pettis
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finite-dimensional decomposition
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