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Weakly Lindelof determined Banach spaces not containing $\ell^1(N)$

Spiros A. Argyros
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Abstract

The class of countably intersected families of sets is defined. For any such family we define a Banach space not containing $\ell^{1}(\NN )$. Thus we obtain counterexamples to certain questions related to the heredity problem for W.C.G. Banach spaces. Among them we give a subspace of a W.C.G. Banach space not containing $\ell^{1}(\NN )$ and not being itself a W.C.G. space.

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Spiros A. Argyros. 1992-10-30. Weakly Lindelof determined Banach spaces not containing $\ell^1(N)$. https://arxiv.org/abs/math/9210210

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