Cones with bounded and unbounded bases and reflexivity (Q844970)
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scientific article; zbMATH DE number 5666150
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cones with bounded and unbounded bases and reflexivity |
scientific article; zbMATH DE number 5666150 |
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Cones with bounded and unbounded bases and reflexivity (English)
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5 February 2010
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The authors give two characterizations of reflexivity for a Banach space \(X\). The first one is based on the existence in \(X\) of a closed convex cone with a nonempty interior such that all the bases generated by a strictly positive functional are bounded. The second characterization is given in terms of the nonexistence of a cone such that it has bounded and unbounded bases (both are generated by strictly positive functionals) simultaneously. Such a cone is called a mixed base cone. Then they study the features of this class of cones and give a description of the structure of a mixed based cone.
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reflexive space
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mixed based cone
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cone conically isomorphic to \(\ell _+^1\)
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strongly summing sequence
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