Orthogonally additive operators on lattice-normed spaces. (Russian) Zbl 1050.47501

Kusraev, A. G.; Pliev, M. A.

Vladikavkaz. Mat. Zh. 1, No. 3, 33-43 (1999).

A new class of dominated nonlinear orthogonally additive operators that act on lattice-normed spaces is introduced. Questions of existence and calculation of an explicit majorant of the operator and decomposability of the majorant norm are considered. Laterally continuous and completely additive operators are studied.

Reviewer: S. A. Malyugin (Novosibirsk)

MSC:

47B65	Positive linear operators and order-bounded operators
47H30	Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
46B40	Ordered normed spaces

Keywords:

Uryson operator; vector lattice; order bounded operator