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The Dodds-Fremlin type theorem for abstract Uryson operators

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Vladimir Orlov, Marat Pliev, Dmitry Rode

Functional Analysis · Submitted 20 Oct 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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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arXiv ID1510.05883 (version 1)
Pith IDEJOAHQWZ, Pith's permanent record of this paper and its review
CitationDmitry Rode, Marat Pliev, Vladimir Orlov. "The Dodds-Fremlin type theorem for abstract Uryson operators." arXiv:1510.05883 (2015). https://pith.science/paper/EJOAHQWZ
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,994 input tokens.

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arXiv listing abstract v1. Results and the main claim are underlined; .

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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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We continue the investigation of abstract Uryson operators in vector lattices. background 0.98 0.48 0.02 asserted 0.56
s1 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. method 0.75 0.57 0.03 asserted 0.56
s2 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. result 0.99 0.95 0.96 asserted 1.00

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original 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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