[Banach] Abstract of a paper by Daniel Freeman, Edward Odell, and Thomas Schlumprecht

This is an announcement for the paper "The universality of $\ell_1$ as a dual space" by Daniel Freeman, Edward Odell, and Thomas Schlumprecht.

Abstract: Let $X$ be a Banach space with a separable dual. We prove that $X$ embeds isomorphically into a $\L_\infty$ space $Z$ whose dual is isomorphic to $\ell_1$. If $X$ has a shrinking finite dimensional decomposition and $X^*$ does not contain an isomorph of $\ell_1$, then we construct such a $Z$, as above, not containing an isomorph of $c_0$.If $X$ is separable and reflexive, we show that $Z$ can be made to be somewhat reflexive.

Archive classification: math.FA

Mathematics Subject Classification: 46B20

Remarks: 33 pages

The source file(s), fos3.tex: 130106 bytes, is(are) stored in gzipped form as 0904.0462.gz with size 37kb. The corresponding postcript file has gzipped size 218kb.

Submitted from: schlump@math.tamu.edu

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