Weak* almost Dunford-Pettis operators in Banach lattices

Abstract

By introducing the concepts of order almost Dunford-Pettis and almost weakly limited operators in Banach lattices, we give some properties of them related to some well known classes of operators, such as, order weakly compact, order Dunford-Pettis, weak and almost Dunford-Pettis and weakly limited operators. Then, we characterize Banach lattices E and F on which each operator from E into F that is order almost Dunford-Pettis and weak almost Dunford-Pettis is an almost weakly limited operator.

Extensões biduais de operadores lineares e multilineares entre espaços de Riesz e reticulados de Banach

“…A contrapartida dessa importante classe de operadores no contexto de reticulados de Banach são os operadores quase Dunford-Pettis, que são aqueles que transformam sequências disjuntas fracamente nulas do domínio em sequências nulas em norma no contradomínio. Os operadores lineares quase Dunford-Pettis atraíram a atenção de muitos especialistas, veja por exemplo [8,20,42,48,67,70,71,72].…”