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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on asymptotically isometric copies of $l^1$ and $c_0$


Author: Hermann Pfitzner
Journal: Proc. Amer. Math. Soc. 129 (2001), 1367-1373
MSC (2000): Primary 46B03, 46B04, 46B20, 47H10
Published electronically: October 20, 2000
MathSciNet review: 1814162
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Abstract:

Nonreflexive Banach spaces that are complemented in their bidual by an L-projection--like preduals of von Neumann algebras or the Hardy space $H^1$--contain, roughly speaking, many copies of $l^1$ which are very close to isometric copies. Such $l^1$-copies are known to fail the fixed point property. Similar dual results hold for $c_0$.


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Additional Information

Hermann Pfitzner
Affiliation: Université d’Orléans, BP 6759, F-45067 Orléans Cedex 2, France
Email: pfitzner@labomath.univ-orleans.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05786-5
PII: S 0002-9939(00)05786-5
Keywords: Asymptotically isometric copies of $l_1$, James' distortion, L-summands, L-embedded, M-ideals, fixed point property
Received by editor(s): July 20, 1999
Published electronically: October 20, 2000
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society