The cofinal property of the reflexive indecomposable Banach spaces

Argyros, Spiros A.; Raikoftsalis, Theocharis

Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 1-45.

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.

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.

Classification : 46B03, 46B06, 46B70
Keywords: Banach space theory, $\ell _p$ saturated, indecomposable spaces, hereditarily indecomposable spaces, interpolation methods, saturated norms
Mots clés : espace de Banach, $\ell _p$-saturé, espaces indécomposables, espaces héréditairement indécomposables, méthodes d’interpolation, normes saturées

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