We consider convex versions of the strong approximation property and the weak bounded approximation property and develop a unified approach to their treatment introducing the inner and outer Λ-bounded approximation properties for a pair consisting of an operator ideal and a space ideal. We characterize this type of properties in a general setting and, using the isometric DFJP-factorization of operator ideals, provide a range of examples for this characterization, eventually answering a question due to Lima, Lima, and Oja: Are there larger Banach operator ideals than 𝒲 yielding the weak bounded approximation property?
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-3-2,
author = {Aleksei Lissitsin},
title = {A unified approach to the strong approximation property and the weak bounded approximation property of Banach spaces},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {199-214},
zbl = {1275.46009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-3-2}
}
Aleksei Lissitsin. A unified approach to the strong approximation property and the weak bounded approximation property of Banach spaces. Studia Mathematica, Tome 209 (2012) pp. 199-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-3-2/