Finite elements in some vector lattices of nonlinear operators

We study the collection of finite elements Φ 1(U(E, F)) in the vector lattice U(E, F) of orthogonally additive, order bounded (called abstract Uryson) operators between two vector lattices E and F, where F is Dedekind complete. In particular, for an atomic vector lattice E it is proved that for a finite element in φ∈ U(E, R) there is only a finite set of mutually disjoint atoms, where φ does not vanish and, for an atomless vector lattice the zero-vector is the only finite element in the band of σ-laterally continuous abstract Uryson functionals. We also describe the ideal Φ 1(U(Rn, Rm)) for n, m∈ N and consider rank one operators to be finite elements in U(E, F). © 2017, Springer International Publishing AG.

Авторы
Pliev M.A. 1, 2 , Weber M.R.3
Редакторы
-
Журнал
Издательство
Birkhauser Verlag AG
Номер выпуска
1
Язык
Английский
Страницы
245-260
Статус
Опубликовано
Подразделение
-
Номер
-
Том
22
Год
2018
Организации
  • 1 Southern Mathematical Institute, Russian Academy of Sciences, Str. Markusa 22, Vladikavkaz, 362027, Russian Federation
  • 2 RUDN University, 6 Miklukho-Maklaya Str, Moscow, 117198, Russian Federation
  • 3 Department of Mathematics, Institute of Analysis, Technical University Dresden, Dresden, 01062, Germany
Ключевые слова
Finite elements; Orthogonally additive order bounded operators; Rank-one operators; Uryson operators
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6814/