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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

Sophocles Mercourakis
Affiliation: Department of Mathematics, University of Athens, Athens 15784, Greece

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

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