Every lateral band is the kernel of an orthogonally additive operator
Автор: Pliev Marat A.
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 4 т.23, 2021 года.
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In this paper we continue a study of relationships between the lateral partial order ⊑ in a vector lattice (the relation x⊑y means that x is a fragment of y) and the theory of orthogonally additive operators on vector lattices. It was shown in [1] that the concepts of lateral ideal and lateral band play the same important role in the theory of orthogonally additive operators as ideals and bands play in the theory for linear operators in vector lattices. We show that, for a vector lattice E and a lateral band G of E, there exists a vector lattice F and a positive, disjointness preserving orthogonally additive operator T:E→F such that kerT=G. As a consequence, we partially resolve the following open problem suggested in [1]: Are there a vector lattice E and a lateral ideal in E which is not equal to the kernel of any positive orthogonally additive operator T:E→F for any vector lattice F?
Orthogonally operator, lateral ideal, lateral band, lateral disjointness, orthogonally additive projection, vector lattice
Короткий адрес: https://sciup.org/143177814
IDR: 143177814 | DOI: 10.46698/e4075-8887-4097-s
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