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.
We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.
We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences.
We establish some properties of the class of order weakly compact operators on Banach lattices. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms.
An application of Mittag-Leffler lemma in the category of quotients of Fréchet spaces. We use Mittag-Leffler Lemma to prove that for a nonempty interval ]a, b[⊂ R, the restriction mapping H∞(]a, b[+iR) → C∞ (]a, b[) is surjective and we give a corollary.