A Gelfand-Phillips space not containing \(\ell_1\) whose dual ball is not weak\(^*\) sequentially compact (Q2710436)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Gelfand-Phillips space not containing \(\ell_1\) whose dual ball is not weak\(^*\) sequentially compact |
scientific article |
Statements
1 March 2002
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Gelfand-Phillips property
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Banach spaces not containing \(\ell_{1}\)
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weak\(^*\) sequentially compact dual ball
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A Gelfand-Phillips space not containing \(\ell_1\) whose dual ball is not weak\(^*\) sequentially compact (English)
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A set \(D\) in a Banach space \(E\) is limited if pointwise convergent sequences of linear functionals converge uniformly on \(D \) and \(E\) has the Gelfand-Phillips property (GPP) if every limited set in \(E\) is relatively compact. It is known that Banach spaces with weak\(^*\) sequentially compact dual balls have the GPP, and \(\ell_{1}(\Gamma)\) has the GPP without having a weak\(^*\) sequentially compact dual ball. In this paper an example of Hagler and Odell is modified to yield a Banach space as described in the title of this note.
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