On extensions of some nonlinear maps in vector lattices

We show that an Urysohn lattice pre-homomorphism defined on a normal sublattice D of a vector lattice E can be extended to the whole space E and the extended operator is an Urysohn lattice homomorphism. We introduce a new class of nonlinear operators which called φ-operators and describe some of their properties. Finally we investigate a structure of positive orthogonally additive operators dominated by an Urysohn lattice homomorphism defined on a vector lattice E and taking value in Dedekind complete vector lattice F. © 2017 Elsevier Inc.

Авторы
Abasov N. 1, 2, 3 , Pliev M. 1, 2, 3
Редакторы
-
Издательство
Academic Press Inc.
Номер выпуска
1
Язык
Английский
Страницы
516-527
Статус
Опубликовано
Подразделение
-
Номер
-
Том
455
Год
2017
Организации
  • 1 MAI – Moscow Aviation Institute, National Research University, str. Orshanskaya 3, Moscow, 121552, Russian Federation
  • 2 Southern Mathematical Institute of the Russian Academy of Sciences, str. Markusa 22, Vladikavkaz, 362027, Russian Federation
  • 3 RUDN University, 6 Miklukho-Maklaya st, Moscow, 117198, Russian Federation
Ключевые слова
Abstract Urysohn operator; Normal sublattice; Orthogonally additive operator; Urysohn lattice homomorphism; Vector lattice; φ-Operator
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5230/