We show that a Banach space X has the compact approximation property if and only if for every Banach space Y and every weakly compact operator T: Y → X, the space = S ∘ T: S compact operator on X is an ideal in = span(,T) if and only if for every Banach space Y and every weakly compact operator T: Y → X, there is a net of compact operators on X such that and in the strong operator topology. Similar results for dual spaces are also proved.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-2-6,
author = {Vegard Lima and \AA svald Lima and Olav Nygaard},
title = {On the compact approximation property},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {185-200},
zbl = {1068.46015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-2-6}
}
Vegard Lima; Åsvald Lima; Olav Nygaard. On the compact approximation property. Studia Mathematica, Tome 162 (2004) pp. 185-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-2-6/