The universality of ${\ell }_1$ as a dual space

Abstract

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.

30 pages