Ideals of finite rank operators, intersection properties of balls, and the approximation property
Studia Mathematica, Tome 133 (1999) no. 2, pp. 175-186
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of $c_0$, the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E).
@article{10_4064_sm_133_2_175_186,
author = {\r{A}svald Lima and },
title = {Ideals of finite rank operators, intersection properties of balls, and the approximation property},
journal = {Studia Mathematica},
pages = {175--186},
publisher = {mathdoc},
volume = {133},
number = {2},
year = {1999},
doi = {10.4064/sm-133-2-175-186},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-133-2-175-186/}
}
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%0 Journal Article %A Åsvald Lima %A %T Ideals of finite rank operators, intersection properties of balls, and the approximation property %J Studia Mathematica %D 1999 %P 175-186 %V 133 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-133-2-175-186/ %R 10.4064/sm-133-2-175-186 %G en %F 10_4064_sm_133_2_175_186
Åsvald Lima; . Ideals of finite rank operators, intersection properties of balls, and the approximation property. Studia Mathematica, Tome 133 (1999) no. 2, pp. 175-186. doi: 10.4064/sm-133-2-175-186
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