The canonical seminorm on Weak L¹
The dual locale of a seminormed space
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 equicontinuous week* topology and semi-reflexivity
The Finest Nachbin Topology is a Mixed Topology.
The Hahn-Banach property and equivalent conditions
The Kreps-Yan theorem for Banach ideal spaces.
The locally convex -spaces and their dual spaces.
The Mackey-Arens and Hahn-Banach theorems for spaces over valued fields
The precompactness–lemma
The separated extensional Chu category.
The Sobolev spaces of harmonic functions
The uniform classification of boundedly compact locally convex spaces
Theoremes of the Orlicz-Pettis-Type for Locally Convex Spaces.
Topological -autonomous categories.
Topological classification of strong duals to nuclear (LF)-spaces
We show that the strong dual X’ to an infinite-dimensional nuclear (LF)-space is homeomorphic to one of the spaces: , , , , or , where and . In particular, the Schwartz space D’ of distributions is homeomorphic to . As a by-product of the proof we deduce that each infinite-dimensional locally convex space which is a direct limit of metrizable compacta is homeomorphic either to or to . In particular, the strong dual to any metrizable infinite-dimensional Montel space is homeomorphic either...
Topological dual of non-locally convex Orlicz-Bochner spaces
Let be an Orlicz-Bochner space defined by an Orlicz function taking only finite values (not necessarily convex) over a -finite atomless measure space. It is proved that the topological dual of can be represented in the form: , where and denote the order continuous dual and the singular dual of respectively. The spaces , and are examined by means of the H. Nakano’s theory of conjugate modulars. (Studia Mathematica 31 (1968), 439–449). The well known results of the duality theory...
Topological proper separation theorems
Topologies et bornologies nucléaires associées. Applications
Le présent article est consacré à l’étude de la topologie nucléaire associée à une topologie localement convexe séparée arbitraire et ses applications. On utilise des techniques de Bornologie. On établit que tout espace ultra-bornologique, en particulier tout espace de Banach, est dual fort d’un espace nucléaire complet et on donne quelques applications de ce résultat. Nous montrons l’existence d’une large classe d’espaces nucléaires complets à bornés métrisables et à duals forts non nucléaires...