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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## The Banach space $S$ is complementably minimal and subsequentially prime

### Tom 156 / 2003

Studia Mathematica 156 (2003), 227-242 MSC: 46B03, 46B20. DOI: 10.4064/sm156-3-2

#### Streszczenie

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).

#### Autorzy

• G. AndroulakisDepartment of Mathematics
University of South Carolina
Columbia, SC 29208, U.S.A.
e-mail
• T. SchlumprechtDepartment of Mathematics
Texas A&M University
College Station, TX 77843, U.S.A.
e-mail

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