Cet article est une étude des rapports entre les propriétés d’intersection et l’existence des grandes faces pour les boules d’un espace de Banach. D’après un résultat classique de Hanner un espace de dimension finie a la propriété d’intersection 3.2 (la “p.i. 3.2”) si et seulement si deux faces disjointes quelconques sont contenues dans deux hyperplans parallèles. Nous donnons ici une démonstration pour le cas général. Nous prouvons aussi que l’espace des opérateurs compacts de dans a la p.i. 3.2 si et seulement si et ont la p.i. 3.2 et de plus ou bien ou bien est isométrique à un espace .
We study the connection between intersection properties of balls and the existence of large faces of the unit ball in Banach spaces. Hanner’s result that a real space has the 3.2 intersection property if an only if disjoint faces of the unit ball are contained in parallel hyperplanes is extended to infinite dimensional spaces. It is shown that the space of compact operators from a space to a space has the 3.2 intersection property if and only if and have the 3.2 intersection property and either or is isometric to an -space.
@article{AIF_1978__28_3_35_0,
author = {Lima, Asvald},
title = {Intersection properties of balls in spaces of compact operators},
journal = {Annales de l'Institut Fourier},
pages = {35--65},
publisher = {Institut Fourier},
address = {Grenoble},
volume = {28},
number = {3},
year = {1978},
doi = {10.5802/aif.700},
zbl = {0347.46018},
mrnumber = {80g:47048},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.700/}
}
TY - JOUR AU - Lima, Asvald TI - Intersection properties of balls in spaces of compact operators JO - Annales de l'Institut Fourier PY - 1978 SP - 35 EP - 65 VL - 28 IS - 3 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.700/ DO - 10.5802/aif.700 LA - en ID - AIF_1978__28_3_35_0 ER -
%0 Journal Article %A Lima, Asvald %T Intersection properties of balls in spaces of compact operators %J Annales de l'Institut Fourier %D 1978 %P 35-65 %V 28 %N 3 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.700/ %R 10.5802/aif.700 %G en %F AIF_1978__28_3_35_0
Lima, Asvald. Intersection properties of balls in spaces of compact operators. Annales de l'Institut Fourier, Tome 28 (1978) no. 3, pp. 35-65. doi : 10.5802/aif.700. https://aif.centre-mersenne.org/articles/10.5802/aif.700/
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