On Orthogonally Additive Operators in Lattice-Normed Spaces
Nonna Dzhusoeva, S. Yu. Itarova
Abstract
In this paper, we study a new class of locally dominated orthogonally additive operators on lattice-normed spaces (LNS). In the first part of the paper, sufficient conditions for the existence of a local exact majorant of a locally dominated operator and formulas for its calculation are given. The second part shows that the $$C$$ -compactness of a dominated orthogonally additive operator acting from a decomposable lattice-normed space to a Banach space with mixed norm implies the $$C$$ -compactness of its exact majorant.
Topics & Concepts
MathematicsCompact spaceCompact operatorNormed vector spaceNorm (philosophy)Lattice (music)Banach spaceOperator normPure mathematicsCompact operator on Hilbert spaceFinite-rank operatorOperator theoryDual normApproximation propertyOperator (biology)Discrete mathematicsPhysicsAcousticsTranscription factorComputer scienceProgramming languagePolitical scienceBiochemistryRepressorGeneChemistryLawExtension (predicate logic)Advanced Banach Space TheoryApproximation Theory and Sequence SpacesFixed Point Theorems Analysis