Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 12, Number 3 (2018), 730-750.
Disjointness-preserving orthogonally additive operators in vector lattices
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 , taking values in a Dedekind-complete vector lattice . We conclude by obtaining an analytical representation for a nonlinear lattice homomorphism between order ideals of spaces of measurable almost everywhere finite functions.
Banach J. Math. Anal., Volume 12, Number 3 (2018), 730-750.
Received: 29 August 2017
Accepted: 10 January 2018
First available in Project Euclid: 16 June 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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