Le groupe des isométries d'un espace de Banach
Le problème des 3 espaces : un contre-exemple de J. Lindenstrauss
Le problème des enveloppes
Le théorème de Dvoretzky
Le théorème de Dvoretzky (suite)
Les espaces de type et cotype 2 d'après Bernard Maurey, et leurs applications
On définit et étudie les espaces de Banach de type et de cotype , . Cela permet de dire que, dès que certaines applications sont -sommantes, elles sont aussi -sommantes pour .
Les espaces faiblement lisses et les espaces strictement quadratiques
Les points extremes et les points unis de la boule unitée étudiés au moyen du semi-produit scalaire
Les systémes orthonormaux dans des espaces vectoriels normés
Les topologies sygma-Lebesgue sur C(X).
We prove that if X is a compact topological space which contains a nontrivial metrizable connected closed subset, then the vector lattice C(X) does not carry any sygma-Lebesgue topology.
L'espace usuel C ne possede aucun R.U.C-systeme orthonorme.
Lévy-Khinchine representation and Banach spaces of type and cotype
Lifting of certain isomorphic properties to .
Lifting Properties for Some Quotients of L1-Spaces and Other Spaces L-Summand in Their Bidual.
Limit points of arithmetic means of sequences in Banach spaces
We shall prove the following statements: Given a sequence in a Banach space enjoying the weak Banach-Saks property, there is a subsequence (or a permutation) of the sequence such that whenever belongs to the closed convex hull of the set of weak limit points of . In case has the Banach-Saks property and is bounded the converse assertion holds too. A characterization of reflexive spaces in terms of limit points and cores of bounded sequences is also given. The motivation for the...
Limited -converging operators and relation with some geometric properties of Banach spaces
By using the concepts of limited -converging operators between two Banach spaces and , -sets and -limited sets in Banach spaces, we obtain some characterizations of these concepts relative to some well-known geometric properties of Banach spaces, such as -Dunford–Pettis property of order and Pelczyński’s property of order , .
Limiting real interpolation methods for arbitrary Banach couples
We study limiting K- and J-methods for arbitrary Banach couples. They are related by duality and they extend the methods already known in the ordered case. We investigate the behaviour of compact operators and we also discuss the representation of the methods by means of the corresponding dual functional. Finally, some examples of limiting function spaces are given.
Lineability of functionals and operators
This article is divided into two parts. The first one is on the linear structure of the set of norm-attaining functionals on a Banach space. We prove that every Banach space that admits an infinite-dimensional separable quotient can be equivalently renormed so that the set of norm-attaining functionals contains an infinite-dimensional vector subspace. This partially solves a question proposed by Aron and Gurariy. The second part is on the linear structure of dominated operators. We show that the...
Linear functionals on Orlicz sequence spaces without local convexity.
Linear isometries of finite codimensions on Banach algebras of holomorphic functions.