The universality of $\ell_1$ as a dual space

Details The universality of $\ell_1$ as a dual space The universality of $\ell_1$ as a dual space

2009-04-02

arxiv.org/abs/0904.0462v2

Mathematics

Functional Analysis

30 pages

Scientific paper

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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