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 , 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{bwmeta1.element.bwnjournal-article-smv133i2p175bwm,
author = {\AA svald Lima and Eve Oja},
title = {Ideals of finite rank operators, intersection properties of balls, and the approximation property},
journal = {Studia Mathematica},
volume = {133},
year = {1999},
pages = {175-186},
zbl = {0930.46020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv133i2p175bwm}
}
Lima, Åsvald; Oja, Eve. Ideals of finite rank operators, intersection properties of balls, and the approximation property. Studia Mathematica, Tome 133 (1999) pp. 175-186. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv133i2p175bwm/
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