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arxiv: 0904.0462 · v2 · submitted 2009-04-02 · 🧮 math.FA

The universality of ell₁ as a dual space

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keywords spacedualincomparablereflexiveseparabletotallybanachconstruct
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Let $X$ be a Banach space with a separable dual. We prove that $X$ embeds isomorphically into a $\cL_\infty$ space $Z$ whose dual is isomorphic to $\ell_1$. If, moreover, $U$ is a space so that $U$ and $X$ are totally incomparable, then we construct such a $Z$, so that $Z$ and $U$ are totally incomparable. If $X$ is separable and reflexive, we show that $Z$ can be made to be somewhat reflexive.

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