Quelques proprietes des espaces de Banach stables

We prove that stable Banach spaces, introduced by J. L. Krivine and B. Maurey [7], are weakly sequentially complete and that every spreading model defined on a stable Banach space is stable.      

Quelques proprietes des systemes dynamiques qui se decomposent en un produit de deux systemes dont l’un est un schema de Bernoulli

The purpose of this paper is to investigate some properties of dynamical systems that split into the product of two systems, one of them being a Bernoulli shift. With this view in mind, a relative version of the main results of D. S. Ornstein’s theory of Bernoulli shifts is developed here.     

Quelques proprietes des applications de trace dance des espaces de champs de vecteurs a divergence nulle

In many problems arising in cotinuum mechanics, and particularly in the study of icompressible fluids, divergence–free vector fields are used as variational spaces.

The boundary conditions met by the weak solutions of such problems are implicitly contained in the variational equation, but the divergence condition makes them very difficult to obtain.

We give here a characterization of the traces (in the sense of Sobolev space' theory) of divergence–free vector fields on the boundary of the reference domain; this provides a useful tool to get the above–mentionned boundary conditions, which are necessary at least in the regularity study of solutions.     

Quelques proprietes des systemes generateurs minimaux des monoides

In this paper we give some results about minimal generating systems of a monoïd M. The main tool is a relation denoted “S” which is finer than the relation “J”.     

Quelques proprietes des espaces homogenes spheriques

Let G be a connected, reductive, algebraic group on an algebraically closed field k of characteristic zero. Let H be aspherical subgroup of G, i.e. H is a closed subgroup of G such that every Borel subgroup of G operates on G/H with an open orbit.It is shown that for a spherical subgroup H, the homogeneous space G/H is a deformation of a homogeneous space G/H₀, where H₀ contains a maximal unipotent subgroup of G (such a H₀ is spherical). It is also shown that every Borel subgroup of G has a finite number of orbits in G/H.     

Quelques Remarques sur un Produit Tensoriel d'Opérateurs

Sans résuméCette note a été préparée pendant que l'auteur était boursier de la Fondation d'Alexander von Humboldt.     

Quelques resultats d'entropie sur l'espace de Wiener

One studies three problems related to entropy phenomenon in the classical Wiener space. In particular, the minoration of the Wiener measure for the set {xX/(x)} is given where is a Sobolev norm in the Wiener spaceX.

     

Transformation de Fourier des distributions de type positif sur un groupe de Lie unimodulaire

Call a locally compact group G, C¹-unique, if L¹(G) has exactly one (separating) C¹-norm. It is easy to see that a ¹-regular group G is C¹-unique and that a C¹-unique group is amenable. For connected groups G it is proved that G is C¹-unique, if the interior R(G)⁰ of a certain part R(G) of Prim(G), called the regular part of Prim(G), is dense in Prim(G), and that C¹-uniqueness of G implies the density of R(G) in Prim(G). From this it is derived that a connected group of type I is C¹-unique if and only if R(G)⁰ is dense in Prim(G). For exponential G, a quite explicit version of this result in terms of the Lie algebra of G is given. As an easy consequence, examples of amenable groups, which are not C¹-unique, and C¹-unique groups, which are not ¹-regular are obtained. Furthermore it is shown that a connected locally compact group G is amenable if and only if L¹(G) has exactly one C¹-norm, which is invariant under the isometric ¹-automorphisms of L¹(G).     

Etude de la categorie des algebres de Hopf commutatives connexes sur un corps

Let k be a perfect field of characteristic p0; the categoryH of connected abelian Hopf algebras over k is abelian and locally noetherian. Technics of locally noetherian categories are used here to obtain Krull and homological dimensions ofH (which are respectively 1 and 2), and a decomposition ofH in a product of categories. First we have, whereH ^– is the category of Grassman algebras, andH ⁺ consists of Hopf algebras which are zero in odd degrees; then we prove thatH ⁺ itself is a product of isomorphic categoriesH _n, n^*, and we give an equivalence betweenH _n and a category of modules. This is compared to some results of algebraic geometry about Greenberg modules.