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 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 ensembles de fermetures sur un ensemble ordonne

L'exposé contient deux résultats principaux. Le premier est une caractérisation de la décomposition canonique d'une fermeture par deux conditions. Le second donne une condition nécessaire et suffisante pour que l'ensemble des fermetures supérieures d'un ensemble ordonné E soit un sous inf-demi treillis complet de l'ensemble des parties de E.     

Espaces de Banach stables

We define the notion of “stable Banach space” by a simple condition on the norm. We prove that ifE is a stable Banach space, then every subspace ofL ^p(E) (1≦p<∞) is stable. Our main result asserts that every infinite dimensional stable Banach space containsl ^p, for somep, 1≦p<∞. This is a generalization of a theorem due to D. Aldous: every infinite dimensional subspace ofL ¹ containsl ^p, for somep in the interval [1, 2].     

La structure des espaces de Banach reticules ayantla propriete de Radon-Nikodym

A separable Banach lattice has the Radon-Nikodym property if and only if it is isometrically the dual of a Banach lattice.     

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”.     

Sur la loi forte des grands nombres dans les espaces de Banach

Sans résumé     

Espaces de Banach superstables,distances stables et homeomorphismes uniformes

We introduce here the notion of superstable Banach space, as the superproperty associated with the stability property of J. L. Krivine and B. Maurey. IfE is superstable, so are theL ^p (E) for eachp∈[1, +∞[. If the Banach spaceX uniformly imbeds into a superstable Banach space, then there exists an equivalent invariant superstable distance onX; as a consequenceX contains subspaces isomorphic tol ^p spaces (for somep∈[1, ∞[). We give also a generalization of a result of P. Enflo: the unit ball ofc ₀ does not uniformly imbed into any stable Banach space.     

Sur les espaces de Banach contenantl 1(τ)

Letτ be a cardinal with cf(τ)>ℵ₀. Then a Banach spaceE contains a subspace isomorphic tol ^l(τ) if and only if [0,1] ^r is a continuous image of the unit ballE′₁ ofE′, provided with the w*-topology. It follows that, for each cardinalκ, ifE′₁ contains a copy ofβκ, thenE has a quotient isomorphic tol ^∞(κ). In this situation we show thatE has even a quotientisometric tol ^∞(κ).      

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.     

Sur la topologie des espaces de fonctions holomorphes

Sans résuméA MonsieurG. Köthe pour son 60e anniversaire     

Localisation et multiplicateurs des espaces de Sobolev homogenes

Sans résumé     

Quelques applications des résolvantes de Ray

Sans résumé