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Decomposition of an abstract Uryson operator
M. A. Ben Amor, M. Pliev
We consider the space of abstract Uryson operators firstly introduced in [9]. We obtain the formulas for band projections on the band generated by increasing set of a positive Urys…
Dominated Uryson operators on lattice-normed spaces
Marat Pliev, Batradz Tasoev
The aim of this note is to introduce the space D_{U}(V,W) of the dominated Uryson operators on lattice-normed spaces. We prove an "Up-and-down" type theorem for a positive abstract…
Narrow operators on lattice-normed spaces
M. Pliev
The aim of this article is to extend results of Maslyuchenko O., Mykhaylyuk V. Popov M. about narrow operators on vector lattices. We give a new definition of a narrow operator whe…
Narrow orthogonally additive operators
Marat Pliev, Mikhail Popov
We extend the notion of narrow operators to nonlinear maps on vector lattices. The main objects are orthogonally additive operators and, in particular, abstract Uryson operators. M…