Separable quotients of Banach spaces.
In this survey we show that the separable quotient problem for Banach spaces is equivalent to several other problems for Banach space theory. We give also several partial solutions to the problem.
Series Representations of Linear Functionals.
Set quantities and Tauberian operators.
Sets with the Radon-Nikodým property in conjugate Banach space
Smooth and R-analytic negligibility of subsets and extension of homeomorphisms in Banach spaces
Smooth partitions of unity in preduals of WCG spaces.
Snarked sums of Banach spaces.
Some approximation results in Musielak-Orlicz spaces
We prove the continuity in norm of the translation operator in the Musielak-Orlicz spaces. An application to the convergence in norm of approximate identities is given, whereby we prove density results of the smooth functions in , in both the modular and norm topologies. These density results are then applied to obtain basic topological properties.
Some duality results on bounded approximation properties of pairs
The main result is as follows. Let X be a Banach space and let Y be a closed subspace of X. Assume that the pair has the λ-bounded approximation property. Then there exists a net of finite-rank operators on X such that and for all α, and and converge pointwise to the identity operators on X and X*, respectively. This means that the pair (X,Y) has the λ-bounded duality approximation property.
Some Examples Concerning Rotundity in Banach Spaces.
Some properties of monotone type multivalued operators in Banach spaces
Some properties of monotone type multivalued operators including accretive operators and the duality mapping are studied in connection with the structure of Banach spaces.
Some properties of weakly countably determined Banach spaces
Some remarks on subspaces of weakly compactly generated Banach spaces
Some remarks on the duality mapping
Some results in representable Banach spaces.
Some results are presented, concerning a class of Banach spaces introduced by G. Godefroy and M. Talagrand, the representable Banach spaces. The main aspects considered here are the stability in forming tensor products, and the topological properties of the weak* dual unitball.
Some results on submodules of
Some results on intersection properties of balls in complex Banach spaces
Somme Ponctuelle D'operateurs Maximaux Monotones Pointwise Sum of two Maximal Monotone Operators
∗ Cette recherche a été partiellement subventionnée, en ce qui concerne le premier et le dernier auteur, par la bourse OTAN CRG 960360 et pour le second auteur par l’Action Intégrée 95/0849 entre les universités de Marrakech, Rabat et Montpellier.The primary goal of this paper is to shed some light on the maximality of the pointwise sum of two maximal monotone operators. The interesting purpose is to extend some recent results of Attouch, Moudafi and Riahi on the graph-convergence of maximal monotone...
Spreading basic sequences and subspaces of James' quasi-reflexive space.
Stable smooth and extreme points, and reflexivity