Representations of Riesz spaces as spaces of measures. I
Representations of Riesz spaces as spaces of measures. II
Representations of the spaces
We give a representation of the spaces as spaces of vector-valued sequences and use it to investigate their topological properties and isomorphic classification. In particular, it is proved that is isomorphic to the sequence space , thereby showing that the isomorphy class does not depend on the dimension N if p=2.
Representations of topological projector dense lattice algebras
Representing and absolutely representing systems
We introduce various classes of representing systems in linear topological spaces and investigate their connections in spaces with different topological properties. Let us cite a typical result of the paper. If H is a weakly separated sequentially separable linear topological space then there is a representing system in H which is not absolutely representing.
Resolution of identity in certain metrizable locally convex spaces.
Resolutions of the identity in certain Banach spaces.
Resolving Banach spaces
Resultados Recientes Sobre Espacios Polinomiales De Tipo Numerable.
Résultats récents sur les formes positives sur des espaces de fonctions
Résumé des résultats essentiels dans la théorie des produits tensoriels topologiques et des espaces nucléaires
L’auteur donne un résumé des résultats essentiels de son travail “Produits tensoriels topologiques et espaces nucléaires” (à paraître dans Memoirs of the Am. Math. Soc.), en essayant de faire ressortir les idées directrices. Soient et deux espaces localement convexes, on définit d’abord deux topologies naturelles sur , qui donnent des complétés et , qu’on explicite dans divers cas importants, et dont on élucide les propriétés algébrico-topologiques, notamment à l’égard de la notion de produit...
Retractions and Open Mappings between Convex Sets.
Retracts of abelian cyclically ordered groups
Revisiting Cauty's proof of the Schauder conjecture.
Richesses du centre d'un espace vectoriel réticulé.
Riesz spaces and the ultrafilter theorem, I
Right inverses for partial differential operators on Fourier hyperfunctions
We characterize the partial differential operators P(D) admitting a continuous linear right inverse in the space of Fourier hyperfunctions by means of a dual (Ω̅)-type estimate valid for the bounded holomorphic functions on the characteristic variety near . The estimate can be transferred to plurisubharmonic functions and is equivalent to a uniform (local) Phragmén-Lindelöf-type condition.
Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces
For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation ∓ and the class...
R-Schauder decompositions. Some applications.