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arXiv · 1507.07549

Domination Problem for Narrow Orthogonally Additive Operators

Marat A. Pliev
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Abstract

The "Up-and-down" theorem which describes the structure of the Boolean algebra of fragments of a linear positive operator is the well known result of the operator theory. We prove an analog of this theorem for a positive abstract Uryson operator defined on a vector lattice and taking values in a Dedekind complete vector lattice. This result we apply to prove that for an order narrow positive abstract Uryson operator $T$ from a vector lattice $E$ to a Dedekind complete vector lattice $F$, every abstract Uryson operator $S:E\to F$, such that $0\leq S\leq T$ is also order narrow.

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Marat A. Pliev. 2015-07-27. Domination Problem for Narrow Orthogonally Additive Operators. https://arxiv.org/abs/1507.07549

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