Let E be a separable Banach space with the λ-bounded approximation property. We show that for each ϵ > 0 there is a Banach space F with a Schauder basis such that E is isometrically isomorphic to a 1-complemented subspace of F and, moreover, the sequence (Tₙ) of canonical projections in F has the properties and . This is a sharp quantitative version of a classical result obtained independently by Pełczyński and by Johnson, Rosenthal and Zippin.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm196-1-1,
author = {Jorge Mujica and Daniela M. Vieira},
title = {Schauder bases and the bounded approximation property in separable Banach spaces},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {1-12},
zbl = {1201.46022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm196-1-1}
}
Jorge Mujica; Daniela M. Vieira. Schauder bases and the bounded approximation property in separable Banach spaces. Studia Mathematica, Tome 196 (2010) pp. 1-12. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm196-1-1/