Реферат: We study operators that carry disjoint bounded subsets of a Banach lattice into compact, weakly compact, and limited subsets of a Banach space. Surprisingly, these operators behave differently from classical compact, weakly compact, and limited operators. Examples demonstrating that these operators differ from the corresponding classical operators are presented. We introduce and study d-Andrews operators, which carry disjoint bounded sets into Dunford–Pettis sets. The domination problem and norm completeness are discussed for the above-mentioned operators. It is shown that, in general, the domination problem for d-limited operators has a negative solution. Natural conditions on the range are provided that yield positive solutions to the domination problem for d-limited and d-Andrews operators. It is shown that the linear spans of d-compact and d-weakly compact positive operators are complete with respect to their enveloping norms. The “almost versions” are also investigated.

Библиографическая ссылка: Emelyanov E.Y. , Erkurşun-Özcan N. , Gorokhova S.G.
d-Operators in Banach Lattices
Siberian Mathematical Journal. 2025. V.66. N6. P.1499 - 1508. DOI: 10.1134/S003744662506014X WOS Scopus РИНЦ OpenAlex

Даты:

Поступила в редакцию:	15 июл. 2025 г.
Принята к публикации:	23 сент. 2025 г.
Опубликована в печати:	24 нояб. 2025 г.
Опубликована online:	24 нояб. 2025 г.

Идентификаторы БД:

Web of science:	WOS:001622319900015
Scopus:	2-s2.0-105022638737
РИНЦ:	84013607
OpenAlex:	W7106517459

Цитирование в БД: Пока нет цитирований

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