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The structure of Lindenstrauss-Pełczyński spaces

Jesús M. F. Castillo, Yolanda Moreno, Jesús Suárez (2009)

Studia Mathematica

Lindenstrauss-Pełczyński (for short ℒ) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides a negative...

The structure of nonseparable Banach spaces with uncountable unconditional bases.

Carlos Finol, Marek Wójtowicz (2005)

RACSAM

Sea X un espacio de Banach con una base incondicional de Schauder no numerable, y sea Y un subespacio arbitrario no separable de X. Si X no contiene una copia isomorfa de l1(J) con J no numerable entonces (1) la densidad de Y y la débil*-densidad de Y* son iguales, y (2) la bola unidad de X* es débil* sucesionalmente compacta. Además, (1) implica que Y contiene subconjuntos grandes formados por elementos disjuntos dos a dos, y una propiedad similar se verifica para las bases incondicionales no numerables...

The structure of quasiasymptotics of Schwartz distributions

Jasson Vindas (2010)

Banach Center Publications

In this article complete characterizations of the quasiasymptotic behavior of Schwartz distributions are presented by means of structural theorems. The cases at infinity and the origin are both analyzed. Special attention is paid to quasiasymptotics of degree -1. It is shown how the structural theorem can be used to study Cesàro and Abel summability of trigonometric series and integrals. Further properties of quasiasymptotics at infinity are discussed. A condition for test functions in bigger spaces...

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