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

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

1992-10-30

arxiv.org/abs/math/9210210v1

Mathematics

Functional Analysis

Scientific paper

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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