We first include a result of the second author showing that the Banach space S is complementably minimal. We then show that every block sequence of the unit vector basis of S has a subsequence which spans a space isomorphic to its square. By the Pełczyński decomposition method it follows that every basic sequence in S which spans a space complemented in S has a subsequence which spans a space isomorphic to S (i.e. S is a subsequentially prime space).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-3-2,
author = {G. Androulakis and T. Schlumprecht},
title = {The Banach space S is complementably minimal and subsequentially prime},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {227-242},
zbl = {1031.46010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-3-2}
}
G. Androulakis; T. Schlumprecht. The Banach space S is complementably minimal and subsequentially prime. Studia Mathematica, Tome 157 (2003) pp. 227-242. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm156-3-2/