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

 

Examples concerning heredity problems of WCG Banach spaces


Authors: Spiros A. Argyros and Sophocles Mercourakis
Journal: Proc. Amer. Math. Soc. 133 (2005), 773-785
MSC (2000): Primary 46B20, 46B26, 03E05
Published electronically: August 20, 2004
MathSciNet review: 2113927
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Abstract: We present two examples of WCG spaces that are not hereditarily WCG. The first is a space with an unconditional basis, and the second is a space $X$ such that $X^{**}$ is WCG and $X^{**}$ does not contain $\ell^1$. The non-WCG subspace $Y$ of $X$ has the additional property that $Y^{**}$ is not WCG and $X/Y$ is reflexive.


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Additional Information

Spiros A. Argyros
Affiliation: Department of Mathematics, National Technical University of Athens, Athens 15780, Greece
Email: sargyros@math.ntua.gr

Sophocles Mercourakis
Affiliation: Department of Mathematics, University of Athens, Athens 15784, Greece
Email: smercour@math.uoa.gr

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07532-X
PII: S 0002-9939(04)07532-X
Keywords: WCG Banach space, unconditional basis, tree
Received by editor(s): July 16, 2003
Received by editor(s) in revised form: October 23, 2003
Published electronically: August 20, 2004
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society