The Dodds-Fremlin type theorem for abstract Uryson operators
Functional Analysis
2015-10-21 v1
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.
Keywords
Cite
@article{arxiv.1510.05883,
title = {The Dodds-Fremlin type theorem for abstract Uryson operators},
author = {Vladimir Orlov and Marat Pliev and Dmitry Rode},
journal= {arXiv preprint arXiv:1510.05883},
year = {2015}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1507.07549