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July 2018 Disjointness-preserving orthogonally additive operators in vector lattices
Nariman Abasov, Marat Pliev
Banach J. Math. Anal. 12(3): 730-750 (July 2018). DOI: 10.1215/17358787-2018-0001

Abstract

In this article, we investigate disjointness-preserving orthogonally additive operators in the setting of vector lattices. First, we present a formula for the band projection onto the band generated by a single positive, disjointness-preserving, order-bounded, orthogonally additive operator. Then we prove a Radon–Nikodým theorem for a positive, disjointness-preserving, order-bounded, orthogonally additive operator defined on a vector lattice E, taking values in a Dedekind-complete vector lattice F. We conclude by obtaining an analytical representation for a nonlinear lattice homomorphism between order ideals of spaces of measurable almost everywhere finite functions.

Citation

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Nariman Abasov. Marat Pliev. "Disjointness-preserving orthogonally additive operators in vector lattices." Banach J. Math. Anal. 12 (3) 730 - 750, July 2018. https://doi.org/10.1215/17358787-2018-0001

Information

Received: 29 August 2017; Accepted: 10 January 2018; Published: July 2018
First available in Project Euclid: 16 June 2018

zbMATH: 06946079
MathSciNet: MR3824749
Digital Object Identifier: 10.1215/17358787-2018-0001

Subjects:
Primary: 47H30
Secondary: 47H99

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.12 • No. 3 • July 2018
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