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Journal of the London Mathematical Society Advance Access originally published online on May 3, 2007
Journal of the London Mathematical Society 2007 75(2):409-419; doi:10.1112/jlms/jdm003
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© 2007 London Mathematical Society

On strongly asymptotic lp spaces and minimality

S. J. Dilworth1,, V. Ferenczi2, Denka Kutzarova3 and E. Odell4

1 Department of Mathematics
University of South Carolina
Columbia, SC 29208
USA
2 Equipe d’Analyse Fonctionnelle
Bôi te 186
Université Paris 6
4, place Jussieu
75252 Paris cedex 05
France
ferenczi{at}ccr.jussieu.fr
3 Institute of Mathematics
Bulgarian Academy of Sciences
Sofia
Bulgaria
Current address:
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL 61801
USA
denka{at}math.uiuc.edu
4 Department of Mathematics
The University of Texas at Austin
1 University Station C1200
Austin, TX 78712-0257
USA
odell{at}math.utexas.edu

Let 1 ≤ p ≤ {infty} and let X be a Banach space with a semi-normalized strongly asymptotic {ell}p basis (ei). If X is minimal and 1 ≤ p < 2, then X is isomorphic to a subspace of {ell}p. If X is minimal and 2 ≤ p < {infty}, or if X is complementably minimal and 1 ≤ p ≤ {infty}, then (ei) is equivalent to the unit vector basis of {ell}p (or c0 if p = {infty}).

dilworth{at}math.sc.edu

2000 Mathematics Subject Classification 46B20 (Primary), 46B15 (Secondary).

The first, third, and fourth authors were supported by the Workshop in Analysis and Probability at Texas A&M University in 2005. Research of the fourth author was partially supported by the National Science Foundation.

Received January 3, 2006; published online May 3, 2007.


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