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.      

Symetries isometriques applications a la dualite des espaces reticules

We show that ifE is a non-reflexive Banach lattice, there exists for everyn a dual of finite even order ofE which contins isometicallyl _n ^/l . We show that itE is a Banach lattice which is isometric to the dual of a Banach spaceX, then the order intervals are σ (E, X)-compact. We prove then that under various conditions, a Banach lattice which is a dual as a Banach space, is a dual as a Banach lattice. In particular, this is true when the predual ofE is unique.      

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

Sans résumé     

Une caractérisation de la propriété de Radon-Nikodym analytique pour les espaces de Banach isomorphes a leur carrés

Sans résumé     

Operateurs essentiellement reguliers dans les espaces de Banach

Given a closed operatorA acting in a Banach spaceX, we define the regular (respectively the essentialy regular) spectrum σ _r (A) (respectively σ _e,r (A)) ofA. We prove that σ _r (A) and σ _e,r (A) are a closed subsets of the classical spectrum σ(A) ofA. Morever ifA is bounded we prove that σ _r (A) and σ _e,r (A)) satisfies the spectral mapping theorem.     

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).      

Localisation et multiplicateurs des espaces de Sobolev homogenes

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Sur la topologie des espaces de fonctions holomorphes

Sans résuméA MonsieurG. Köthe pour son 60e anniversaire     

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.     

La structure des copolyèdres au sens de Stamm

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Représentations des groupes réductifs dans des espaces de cohomologie

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Représentations des groupes réductifs dans des espaces de cohomologie

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Une propriete arithmetique de certains operateurs differentiels

Define and let L(D)=a_i(x)Dⁱ[x][D] be a linear differential operator with polynomial coefficients. G. POLYA for L(D)=D and D. CANTOR for L(D)=P(xD), P[x] proved that if u[[x]] is such that L(D)(u) is a rational function, then u is also a rational function.In this paper, we introduce a new class of linear differential operators with the same property.