On some isomorphism on the category of -spaces.
A version of the Bartle--Graves theorem for temperate functions.
Le ε-Produit des Loo-Espaces par les Quotients Bornologiques
On some Properties of the ε-Product of Nuclear b-spaces
Caractérisations des b-espaces libres.
Spaces of continuous functions taking their values in the ε-product.
Para un b-espacio nuclear N y un b-espacio E demostramos que si X es un espacio compacto entonces los b-espacios C (X,NεE) y NεC (X,E) son isomorfos. El mismo resultado se verifica también si X es un espacio localmente compacto que es numerable en el infinito.
The exactness of the projective limit functor on the category of quotients of Frechet spaces
We give conditions under which the functor projective limit is exact on the category of quotients of Fréchet spaces of L. Waelbroeck [18].
Une application du lemme de Mittag-Leffler dans la categorie des quotients d’espaces de Frechet
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 , the restriction mapping is surjective and we give a corollary.
Les topologies sygma-Lebesgue sur C(X).
We prove that if X is a compact topological space which contains a nontrivial metrizable connected closed subset, then the vector lattice C(X) does not carry any sygma-Lebesgue topology.
Sur les topologies de Lebesgue.
The order -complete vector lattice of AM-compact operators
We establish necessary and sufficient conditions under which the linear span of positive AM-compact operators (in the sense of Fremlin) from a Banach lattice into a Banach lattice is an order -complete vector lattice.
AM-Compactness of some classes of operators
We characterize Banach lattices on which each regular order weakly compact (resp. b-weakly compact, almost Dunford-Pettis, Dunford-Pettis) operator is AM-compact.
La categorie Abelienne des quotients de type
We construct the category of quotients of -spaces and we show that it is Abelian. This answers a question of L. Waelbroeck from 1990.
Some characterizations of weakly compact operator on Banach lattices
We establish necessary and sufficient conditions under which each operator between Banach lattices is weakly compact and we give some consequences.
Some results on order weakly compact operators
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.
Some characterizations of order weakly compact operator
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.
The weak compactness of almost Dunford-Pettis operators
We characterize Banach lattices on which every positive almost Dunford-Pettis operator is weakly compact.
On the equality between some classes of operators on Banach lattices
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.
Some properties of the tensor product of Schwartz εb-spaces.
We define the ε-product of an εb-space by quotient bornological spaces and we show that if G is a Schwartz εb-space and E|F is a quotient bornological space, then their ε-product Gε(E|F) defined in [2] is isomorphic to the quotient bornological space (GεE)|(GεF).
The -weak compactness of weak Banach-Saks operators
We characterize Banach lattices on which every weak Banach-Saks operator is b-weakly compact.
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