Cette Note présente un résultat de densité de type (ABB) pour la topologie forte dans un espace de Banach muni du préordre associé à un cône convexe possédant une base bornée. L'hypothèse de compacité est sensiblement affaiblie et la méthode présentée ici est nouvelle à notre connaissance. Basée sur des propriétés du cône de Bishop–Phelps, elle ne nécessite pas l'utilisation des cônes de dilatation de Hening.
This Note presents a density result of the ABB theorem type for a strong topology of a Banach space equipped with the preorder associated to a convex well-based cone. The hypothesis of compactness is relaxed. Here the technique used is based on properties of the Bishop–Phelps cone, and does not require any property of the Hening dilating cone.
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@article{CRMATH_2009__347_15-16_853_0,
author = {Bourass, Abdelhamid and Lafhim, Lahoussine},
title = {Nouvelle approche du th\'eor\`eme de {ABB}},
journal = {Comptes Rendus. Math\'ematique},
pages = {853--856},
publisher = {Elsevier},
volume = {347},
number = {15-16},
year = {2009},
doi = {10.1016/j.crma.2009.05.010},
language = {fr},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2009.05.010/}
}
TY - JOUR AU - Bourass, Abdelhamid AU - Lafhim, Lahoussine TI - Nouvelle approche du théorème de ABB JO - Comptes Rendus. Mathématique PY - 2009 SP - 853 EP - 856 VL - 347 IS - 15-16 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2009.05.010/ DO - 10.1016/j.crma.2009.05.010 LA - fr ID - CRMATH_2009__347_15-16_853_0 ER -
%0 Journal Article %A Bourass, Abdelhamid %A Lafhim, Lahoussine %T Nouvelle approche du théorème de ABB %J Comptes Rendus. Mathématique %D 2009 %P 853-856 %V 347 %N 15-16 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2009.05.010/ %R 10.1016/j.crma.2009.05.010 %G fr %F CRMATH_2009__347_15-16_853_0
Bourass, Abdelhamid; Lafhim, Lahoussine. Nouvelle approche du théorème de ABB. Comptes Rendus. Mathématique, Tome 347 (2009) no. 15-16, pp. 853-856. doi : 10.1016/j.crma.2009.05.010. http://archive.numdam.org/articles/10.1016/j.crma.2009.05.010/
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