Examples concerning heredity problems of WCG Banach spaces

Argyros, Spiros; Mercourakis, Sophocles

doi:10.1090/S0002-9939-04-07532-X

Examples concerning heredity problems of WCG Banach spaces
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by Spiros A. Argyros and Sophocles Mercourakis PDF

Proc. Amer. Math. Soc. 133 (2005), 773-785 Request permission

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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