DISJOINTNESS-PRESERVING ORTHOGONALLY ADDITIVE OPERATORS IN VECTOR LATTICES

In this article, we investigate disjointness-preserving orthogonally additive operators in the setting of vector lattices. First, we present a formula for the band projection onto the band generated by a single positive, disjointness-preserving, order-bounded, orthogonally additive operator. Then we prove a Radon-Nikodym theorem for a positive, disjointness-preserving, order-bounded, orthogonally additive operator defined on a vector lattice E, taking values in a Dedekind-complete vector lattice F. We conclude by obtaining an analytical representation for a nonlinear lattice homomorphism between order ideals of spaces of measurable almost everywhere finite functions.

Авторы
Abasov N. 1 , Pliev M. 2, 3
Номер выпуска
3
Язык
Английский
Страницы
730-750
Статус
Опубликовано
Том
12
Год
2018
Организации
  • 1 Natl Res Univ, MAI, Str Orshanskaya 3, Moscow 121552, Russia
  • 2 Russian Acad Sci, Southern Math Inst, Str Markusa 22, Vladikavkaz 362027, Russia
  • 3 RUDN Univ, 6 Miklukho Maklaya St, Moscow 117198, Russia
Ключевые слова
orthogonally additive operator; Urysohn lattice homomorphism; disjointness-preserving operator; vector lattice; Boolean algebra
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/7466/
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