Marat Pliev

Disjointness and order projections in the vector lattices of abstract Uryson operators

Projections onto several special subsets in the Dedekind complete vector lattice of orthogonally additive, order bounded (called abstract Uryson) operators between two vector lattices E and F are considered and some new formulas are provided.

Narrow operators on lattice-normed spaces

The aim of this article is to extend results of Maslyuchenko, Mykhaylyuk and Popov about narrow operators on vector lattices. We give a new definition of a narrow operator, where a vector lattice as the domain space of a narrow operator is replaced with a lattice-normed space. We prove that every GAM-compact (bo)-norm continuous linear operator from a Banach-Kantorovich space V to a Banach lattice Y is narrow. Then we show that, under some mild conditions, a continuous dominated operator is narrow if and only if its exact dominant is so.

Finite elements in some vector lattices of nonlinear operators

We study the collection of finite elements

Narrow Operators on Lattice-normed Spaces and Vector Measures

\Phi _{1}\big ({\mathcal {U}}(E,F)\big )

Dominated Uryson operators

Φ1(U(E,F)) in the vector lattice

Dividing measures and narrow operators

{\mathcal {U}}(E,F)