no. 1
The cofinal property of the reflexive indecomposable Banach spaces
Argyros, Spiros A.1 ; Raikoftsalis, Theocharis1
1 National Technical University of Athens Faculty of Applied Sciences Department of Mathematics Zografou Campus, 157 80, Athens (Greece)
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 ℓ p -saturé, où 1<p<+∞, 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 ℓ p -saturated space with 1<p<∞ and of a c 0 saturated space.

DOI : 10.5802/aif.2697
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

Argyros, Spiros A. 1 ; Raikoftsalis, Theocharis 1

1 National Technical University of Athens Faculty of Applied Sciences Department of Mathematics Zografou Campus, 157 80, Athens (Greece) 
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Argyros, Spiros A.; Raikoftsalis, Theocharis. The cofinal property of the reflexive indecomposable Banach spaces. Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 1-45. doi : 10.5802/aif.2697. https://aif.centre-mersenne.org/articles/10.5802/aif.2697/

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