## Banach Journal of Mathematical Analysis

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

### Disjointness-preserving orthogonally additive operators in vector lattices

Nariman Abasov and Marat Pliev

#### 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