Maurey-Rosenthal factorization for \(p\)-summing operators and Dodds-Fremlin domination (Q2919623)
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scientific article; zbMATH DE number 6090241
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maurey-Rosenthal factorization for \(p\)-summing operators and Dodds-Fremlin domination |
scientific article; zbMATH DE number 6090241 |
Statements
4 October 2012
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\(p\)-summing operator
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positive operator
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Banach lattice
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factorization
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Dodds-Fremlin domination
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0.91885734
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0.91493857
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0.90723985
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0.89974487
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0.8828804
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0.8815174
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0.87579465
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Maurey-Rosenthal factorization for \(p\)-summing operators and Dodds-Fremlin domination (English)
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The authors characterize by means of a vector norm inequality the space of operators that factorize through a \(p\)-summing operator from an \(L_r\)-space to an \(L_s\)-space. As an application, they prove a domination result in the sense of Dodds-Fremlin for \(p\)-summing operators on Banach lattices with cotype 2, showing, moreover, that this cannot hold in general for spaces with higher cotype. They also present a new characterization of Banach lattices satisfying a lower 2-estimate in terms of the order properties of 2-summing operators.
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