Banach Journal of Mathematical Analysis

Disjointness-preserving orthogonally additive operators in vector lattices

Nariman Abasov and Marat Pliev

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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.

Article information

Source
Banach J. Math. Anal., Volume 12, Number 3 (2018), 730-750.

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1529114495

Digital Object Identifier
doi:10.1215/17358787-2018-0001

Mathematical Reviews number (MathSciNet)
MR3824749

Zentralblatt MATH identifier
06946079

Subjects
Primary: 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) [See also 45Gxx, 45P05]
Secondary: 47H99: None of the above, but in this section

Keywords
orthogonally additive operator Urysohn lattice homomorphism disjointness-preserving operator vector lattice Boolean algebra

Citation

Abasov, Nariman; Pliev, Marat. Disjointness-preserving orthogonally additive operators in vector lattices. Banach J. Math. Anal. 12 (2018), no. 3, 730--750. doi:10.1215/17358787-2018-0001. https://projecteuclid.org/euclid.bjma/1529114495


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