Application des ultraproduits à l'étude des espaces et des algèbres de Banach
The paper contains some applications of the notion of sets to several classes of operators on Banach lattices. In particular, we introduce and study the class of order -Dunford-Pettis operators, that is, operators from a Banach space into a Banach lattice whose adjoint maps order bounded subsets to an sets. As a sequence characterization of such operators, we see that an operator from a Banach space into a Banach lattice is order -Dunford-Pettis, if and only if for for every weakly null...
Spherical designs constitute sets of points distributed on spheres in a regular way. They can be used to construct finite-dimensional normed spaces which are extreme in some sense: having large projection constants, big or small Banach-Mazur distance to Hilbert spaces or -spaces. These examples provide concrete illustrations of results obtained by more powerful probabilistic techniques which, however, do not exhibit explicit examples. We give a survey of such constructions where the geometric invariants...