The cofinal property of the reflexive indecomposable Banach spaces

Argyros, Spiros A. ; Raikoftsalis, Theocharis

Annales de l'Institut Fourier, Tome 62 (2012), p. 1-45 / Harvested from Numdam

Résumé

On démontre que tout espace de Banach séparable réflexif est quotient d’un espace réflexif héréditairement indécomposable, ce qui implique que tout espace de Banach séparable réflexif est isomorphe à un sous-espace d’un espace réflexif indécomposable. De plus, tout espace de Banach séparable réflexif est quotient d’un espace réflexif complémentablement $\ell _p$-saturé, où $1<p<+\infty $, et d’un espace $c_0$-saturé.

Abstract

It is shown that every separable reflexive Banach space is a quotient of a reflexive hereditarily indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably $\ell _p$-saturated space with $1<p<\infty $ and of a $c_0$ saturated space.

Détail

Publié le : 2012-01-01

MR 2986263 | Zbl 1253.46009

DOI : https://doi.org/10.5802/aif.2697
Classification:  46B03,  46B06,  46B70
Mots clés: espace de Banach, $\ell _p$-saturé, espaces indécomposables, espaces héréditairement indécomposables, méthodes d’interpolation, normes saturées

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