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 -saturé, où , et d’un espace -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 -saturated space with and of a saturated space.
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
@article{AIF_2012__62_1_1_0, author = {Argyros, Spiros A. and Raikoftsalis, Theocharis}, title = {The cofinal property of the reflexive indecomposable {Banach} spaces}, journal = {Annales de l'Institut Fourier}, pages = {1--45}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {62}, number = {1}, year = {2012}, doi = {10.5802/aif.2697}, zbl = {1253.46009}, mrnumber = {2986263}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2697/} }
TY - JOUR AU - Argyros, Spiros A. AU - Raikoftsalis, Theocharis TI - The cofinal property of the reflexive indecomposable Banach spaces JO - Annales de l'Institut Fourier PY - 2012 SP - 1 EP - 45 VL - 62 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2697/ DO - 10.5802/aif.2697 LA - en ID - AIF_2012__62_1_1_0 ER -
%0 Journal Article %A Argyros, Spiros A. %A Raikoftsalis, Theocharis %T The cofinal property of the reflexive indecomposable Banach spaces %J Annales de l'Institut Fourier %D 2012 %P 1-45 %V 62 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2697/ %R 10.5802/aif.2697 %G en %F AIF_2012__62_1_1_0
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. http://www.numdam.org/articles/10.5802/aif.2697/
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