The Riesz-Kantorovich formulae (Q2329008)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Riesz-Kantorovich formulae |
scientific article |
Statements
The Riesz-Kantorovich formulae (English)
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17 October 2019
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The author provides a regular operator \(T\) from \(L_1[0,1]\) to \(C(K)\) for some compact space \(K\) such that the modulus \(|T|\) of \(T\) exists but is not presentable as \(|T|x=\sup\{Ty : -x\le y\le x\}\) for all \(x\in L_1[0,1]\). So the Riesz-Kantorovich formula may fail if the target space is not Dedekind complete.
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Banach lattice
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regular operator
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modulus
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Riesz-Kantorovich formula
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