Inspired by Pełczyński's decomposition method in Banach spaces, we introduce the notion of Schroeder-Bernstein quadruples for Banach spaces. Then we use some Banach spaces constructed by W. T. Gowers and B. Maurey in 1997 to characterize them.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-3-7,
author = {El\'oi Medina Galego},
title = {An Arithmetic Characterization of Decomposition Methods in Banach Spaces Similar to Pe\l czy\'nski's Decomposition Method},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {52},
year = {2004},
pages = {273-282},
zbl = {1109.46010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-3-7}
}
Elói Medina Galego. An Arithmetic Characterization of Decomposition Methods in Banach Spaces Similar to Pełczyński's Decomposition Method. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) pp. 273-282. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-3-7/