Some new results on L-weakly compact sets and applications

The paper is devoted to study the relationship between limited (resp. (L)) sets and L-weakly compact sets, it rests essentially on two parts. In the first one, we introduce and study the operators which send L-weakly compact sets to limited sets and conversely limited sets to L-weakly compact sets. As consequences, we will give some interesting results. In the second part, we look at the dual counterpart on which we give our results about the relationship between (L) sets and L-weakly compact sets.