Unconditional bases and the Radon-Nikodym property
Unconditional biorthogonal wavelet bases in
We prove that a biorthogonal wavelet basis yields an unconditional basis in all spaces with 1 < p < ∞, provided the biorthogonal wavelet set functions satisfy weak decay conditions. The biorthogonal wavelet set is associated with an arbitrary dilation matrix in any dimension.
Unconditional decompositions and local unconditional structures in some subspaces of , 1≤p<2
Unconditional ideals in Banach spaces
We show that a Banach space with separable dual can be renormed to satisfy hereditarily an “almost” optimal uniform smoothness condition. The optimal condition occurs when the canonical decomposition is unconditional. Motivated by this result, we define a subspace X of a Banach space Y to be an h-ideal (resp. a u-ideal) if there is an hermitian projection P (resp. a projection P with ∥I-2P∥ = 1) on Y* with kernel . We undertake a general study of h-ideals and u-ideals. For example we show that...
Unconditional ideals of finite rank operators
Let be a Banach space. We give characterizations of when is a -ideal in for every Banach space in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for the cases when is a -ideal in for every Banach space , when is a -ideal in for every Banach space , and when is a -ideal in for every Banach space .
Unconditionality for m-homogeneous polynomials on
Let χ(m,n) be the unconditional basis constant of the monomial basis , α ∈ ℕ₀ⁿ with |α| = m, of the Banach space of all m-homogeneous polynomials in n complex variables, endowed with the supremum norm on the n-dimensional unit polydisc ⁿ. We prove that the quotient of and √(n/log n) tends to 1 as n → ∞. This reflects a quite precise dependence of χ(m,n) on the degree m of the polynomials and their number n of variables. Moreover, we give an analogous formula for m-linear forms, a reformulation...
Unconditionally convergent polynomials in Banach spaces and related properties.
Our aim is to introduce a new notion of unconditionallity, in the context of polynomials in Banach spaces, that looks directly to the polynomial topology defined on the involved spaces. This notion allows us to generalize some well-known relations of duality that appear in the linear context.
Unconditionally convergent series of compact operators
Unconditionally covering and Dunford-Pettis operators on
Unconditionally p-null sequences and unconditionally p-compact operators
We investigate sequences and operators via the unconditionally p-summable sequences. We characterize the unconditionally p-null sequences in terms of a certain tensor product and then prove that, for every 1 ≤ p < ∞, a subset of a Banach space is relatively unconditionally p-compact if and only if it is contained in the closed convex hull of an unconditionally p-null sequence.
Uncountable sets of unit vectors that are separated by more than 1
Let X be a Banach space. We study the circumstances under which there exists an uncountable set 𝓐 ⊂ X of unit vectors such that ||x-y|| > 1 for any distinct x,y ∈ 𝓐. We prove that such a set exists if X is quasi-reflexive and non-separable; if X is additionally super-reflexive then one can have ||x-y|| ≥ slant 1 + ε for some ε > 0 that depends only on X. If K is a non-metrisable compact, Hausdorff space, then the unit sphere of X = C(K) also contains such a subset; if moreover K is perfectly...
Une caractérisation de la propriété de Radon-Nikodym analytique pour les espaces de Banach isomorphes a leur carrés.
Une caractérisation des simplexes compacts et des cônes réticulés applications
Une classe d'espaces de Banach qui admettent des quotients séparables
Une classe d'espaces de Banach réticulés.
Une GÉnÉralisation Naturelle du Produit Scalaire Dans un Espace NormÉ et son Utilisation
Une nouvelle classe d'espaces de Banach vérifiant le théorème de Grothendieck
Soit un espace et soit un sous-espace réflexif de dimension infinie de . Nous montrons que le quotient vérifie le théorème de Grothendieck, c’est-à-dire que tout opérateur de dans un espace de Hilbert est 1-sommant; par ailleurs, n’est pas un espace . Cela permet de répondre négativement à une question de Lindenstrauss-Pełczyński ainsi qu’à une question similaire de Grothendieck.
Une propriété du convexe topologique vague des probabilités normales sur un espace topologique
Une propriété du type -stable
Une remarque sur les espaces de Banach mesure-compacts