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

Tom 156 / 2003

G. Androulakis, T. Schlumprecht 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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