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arXiv · 1504.08223

On the structure of separable $\mathcal{L}_\infty$-spaces

Spiros A. Argyros·Ioannis Gasparis·Pavlos Motakis
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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 $c_0$.

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Spiros A. Argyros, Ioannis Gasparis, Pavlos Motakis. 2015-04-30. On the structure of separable $\mathcal{L}_\infty$-spaces. https://doi.org/10.1112/s0025579315000492

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