The universality of $\ell_1$ as a dual space

Daniel Freeman; Edward Odell; Thomas Schlumprecht

The universality of $\ell_1$ as a dual space

Functional Analysis 2010-05-17 v2

Authors: Daniel Freeman , Edward Odell , Thomas Schlumprecht

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.

Keywords

Banach space separable dual ℓ_1 cL_∞ space embedding total incomparability reflexive

Cite

@article{arxiv.0904.0462,
  title  = {The universality of $\ell_1$ as a dual space},
  author = {Daniel Freeman and Edward Odell and Thomas Schlumprecht},
  journal= {arXiv preprint arXiv:0904.0462},
  year   = {2010}
}

Comments

30 pages

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