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arXiv · 1510.05883

The Dodds-Fremlin type theorem for abstract Uryson operators

Vladimir Orlov·Marat Pliev·Dmitry Rode
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Abstract

We continue the investigation of abstract Uryson operators in vector lattices. Using the recently proved Up-and-down theorem for order bounded, orthogonally additive operators, we consider the domination problem for AM-compact abstract Uryson operators. We obtain the Dodds-Fremlin type theorem and prove that for an AM- compact positive abstract Uryson operator T from a Banach lattice E to a order continuous Banach lattice F, every abstract Uryson operator S from E to F included between 0 and T is also AM-compact.

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Vladimir Orlov, Marat Pliev, Dmitry Rode. 2015-10-20. The Dodds-Fremlin type theorem for abstract Uryson operators. https://arxiv.org/abs/1510.05883

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