This is an announcement for the paper "On the structure of separable $\mathcal{L}_\infty$-spaces" by Spiros A. Argyros, Ioannis Gasparis and Pavlos Motakis.

Abstract: Based on a construction method introduced by J. Bourgain and F. Delbaen, we give a general definition of a Bourgain-Delbaen space and prove that every infinite dimensional separable $\mathcal{L}_\infty$-space is isomorphic to such a space. Furthermore, we provide an example of a $\mathcal{L}_\infty$ and asymptotic $c_0$ space not containing $c_0$.

Archive classification: math.FA

Mathematics Subject Classification: 46B03, 46B06, 46B07

Remarks: 15 pages

Submitted from: pmotakis@central.ntua.gr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1504.08223

or

http://arXiv.org/abs/1504.08223