5 papers
Reciprocal Dunford--Pettis sets and V-sets in Banach lattices
Jin Xi Chen, Xi Li
In this short note, we show that one cannot differentiate between reciprocal Dunford--Pettis sets and V-sets in a Banach lattice. That is, for a bounded subset of a Banach…
Totally bounded sets in the absolute weak topology
Halimeh Ardakani, Jin Xi Chen
In this paper, almost Dunford-Pettis operators with ranges in are used to identify totally bounded sets in the absolute weak topology. That is, a bounded subset of a Bana…
Disjointly Weak Compactness in Banach Lattices
Bo Xiang, Jin Xi Chen, Lei Li
We give some characterizations of disjointly weakly compact sets in Banach lattices, namely, those sets in whose solid hulls every disjoint sequence converges weakly to zero. As an…
Weak precompactness in Banach lattices
Bo Xiang, Jinxi Chen, Lei Li
We show that the solid hull of every weakly precompact set of a Banach lattice is weakly precompact if and only if every order interval in is weakly precompact, or equivale…
On a Question of Bouras concerning weak compactness of almost Dunford-Pettis sets
Jin Xi Chen, Lei Li
We give a positive answer to the question of K. Bouras [`Almost Dunford-Pettis sets in Banach lattices', \textit{Rend. Circ. Mat. Palermo (2)} \textbf{ 62} (2013), 227--236] concer…