Some characterizations of weakly compact operator on Banach lattices

summary:We establish necessary and sufficient conditions under which each operator between Banach lattices is weakly compact and we give some consequences

The Abelian category of quotients of LF{\mathcal LF}-spaces

summary:We construct the category of quotients of $\mathcal {L}\Im$-spaces and we show that it is Abelian. This answers a question of L. Waelbroeck from 1990