Un théorème d’extrapolation et son application aux suites sommables dans
Una caracterización de los operadores de Fredholm y semi-Fredholm.
Una nota sobre los espacios de Sobolev.
Una nota sobre los espacios de Sobolev anisótropos vectoriales LΓp (E)*.
Una nota sobre los subespacios K-complementados de los espacios escalonados de sucesiones.
Una propiedad de los espacios de Banach que no son casirreflexivos.
Unbounded symmetric homogeneous domains in spaces of operators
Uncomplementability of spaces of compact operators in larger spaces of operators
In the first part of the paper we prove some new result improving all those already known about the equivalence of the nonexistence of a projection (of any norm) onto the space of compact operators and the containment of in the same space of compact operators. Then we show several results implying that the space of compact operators is uncomplemented by norm one projections in larger spaces of operators. The paper ends with a list of questions naturally rising from old results and the results...
Uncomplemented copies of C(K) inside C(K).
Throughout this note, whenever K is a compact space C(K) denotes the Banach space of continuous functions on K endowed with the sup norm. Though it is well known that every infinite dimensional Banach space contains uncomplemented subspaces, things may be different when only C(K) spaces are considered. For instance, every copy of l∞ = C(BN) is complemented wherever it is found. In [5] Pelzcynski found: Theorem 1. Let K be a compact metric space. If a separable Banach space X contains a subspace...
Unconditional and normalised bases
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.