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/