On the converse of Aliprantis and Burkinshaw's theorem (Q865014)
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scientific article; zbMATH DE number 5125396
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the converse of Aliprantis and Burkinshaw's theorem |
scientific article; zbMATH DE number 5125396 |
Statements
On the converse of Aliprantis and Burkinshaw's theorem (English)
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13 February 2007
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The authors' main result is as follows: Let \((E,\tau)\) be a complete locally convex solid lattice. Then the following are equivalent: (1) If \(T\) is a compact positive operator in \(E\) and \(0\leq S\leq T\) then \(S^2\) is compact; (2) either \(\tau\) is Lebesgue, or \(\beta(E,E')\) is Lebesgue, or \(E'\) is discrete.
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compact operator
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Lebesgue topology
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discrete vector lattice
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