On the class of almost order (L) sets and applications

Some characterizations of L-weakly compact sets using the the unbounded absolutely weakly convergence and applications

“…2) =⇒ 4) By the Proposition 3.2 [3] it suffice to prove that T ′ (f n )(x n ) −→ 0 for every sequence (f n ) ⊂ A and every norm bounded uaw-null sequence (x n ) of E. Indeed, let (f n ) ⊂ A and (x n ) a norm bounded uaw-null sequence of E. It follows from our hypothesis that |T (x n )| w −→ 0 and since A is an almost(L)-set then by Theorem 3.11 [6] we have sol(A) is an almost (L)-set and…”

Adjoints and second adjoints of almost Dunford-Pettis operators

“…The lattice counterpart of this important operator ideal is the class of almost Dunford-Pettis operators: an operator from a Banach lattice to a Banach space is almost Dunford-Pettis if it sends disjoint weakly null sequences to norm null sequences; or, equivalently, if it sends positive disjoint weakly null sequences to norm null sequences. Almost Dunford-Pettis operators have attracted the attention of many experts, for recent developments see [4,5,12,13,18,20,21,22].…”

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].…”