The universality of ℓ1\ell_1 as a dual space

preprint2010arXivOpen access

Abstract

Let XX be a Banach space with a separable dual. We prove that XX embeds isomorphically into a $\cL_\infty$ space ZZ whose dual is isomorphic to ℓ1\ell_1. If, moreover, UU is a space so that UU and XX are totally incomparable, then we construct such a ZZ, so that ZZ and UU are totally incomparable. If XX is separable and reflexive, we show that ZZ can be made to be somewhat reflexive.

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