Sur les cones faiblement complets, contenus dans un espace de Banach.
Sur les cônes réticules analytiques
Sur les espaces de Banach réticulés injectifs
Sur les topologies de Lebesgue.
Sur une famille de cônes réticulés avec domination (les -cônes)
Il s’agit de représenter certains cônes réticulés par des cônes adaptés de fonctions continues sur un espace localement compact. Nous étudions le cône des opérateurs positifs majorés par un multiple de l’identité sur un cône réticulé, le représentons et donnons des conditions nécessaires et suffisantes pour qu’il soit riche (théorème d’Urysohn). Quelques illustrations sont données à la fin dans le cadre des espaces de type de Kakutani.
Tensor Products of Banach Lattices.
The -weak compactness of weak Banach-Saks operators
We characterize Banach lattices on which every weak Banach-Saks operator is b-weakly compact.
The boundedness principle for lattice-normed spaces.
The Components of a Positive Operator.
The dual of the cone of all convex functions on a vector space.
The Dual of the Cone of All Convex Functions on a Vector Space. (Short Communication).
The equivalence of Boolean prime ideal theorem and a theorem of functional analysis
The facial structure of the finite dimensional latticial cone.
The Generalized Theory of Perfect Riesz Spaces I.
The Hahn-Banach property and equivalent conditions
The injective hull of an archimedean f-algebra
The measure extension problem for vector lattices
Let be a boundedly -complete vector lattice. If each -valued premeasure on an arbitrary field of subsets of an arbitrary set can be extended to a -additive measure on the generated -field then is said to have the measure extension property. Various sufficient conditions on which ensure that it has this property are known. But a complete characterisation of the property, that is, necessary and sufficient conditions, is obtained here. One of the most useful characterisations is: has the...
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.
The semi- property for normed Riesz spaces
The space of maximal convex sets