most recent 30 from http://mathoverflow.net 2013-05-24T11:52:46Z http://mathoverflow.net/feeds/question/100494 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/100494/preduals-of-ell-1 Jan Vardøen 2012-06-23T23:54:34Z 2012-06-23T23:54:34Z

<p>The space $\ell_1$ has loads of (isomorphic) predulas. They can be as weird as possible but I am interested in Banach lattices.</p> <p>Question: Let $X$ be a Banach lattice with dual isomorphic to $\ell_1$. Must $X$ be isomorphic to $C(K)$ for some countable $K$?</p> <p>Well, the classical Bourgain-Delbaen spaces are not good candidates because they have no copies of $c_0$, hence they are not isomorphic to a Banach lattice (a Banach lattice without a copy of $c_0$ is weakly sequentially complete and weakly sequentially Banach lattices are complemented in their biduals).</p>