The Banach space $S$ is complementably minimal and subsequentially prime
Volume 156 / 2003
Studia Mathematica 156 (2003), 227-242
MSC: 46B03, 46B20.
DOI: 10.4064/sm156-3-2
Abstract
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).
