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ON THE STRUCTURE OF SEPARABLE ${\mathcal{L}}_{\infty }$ -SPACES

  • Spiros A. Argyros (a1), Ioannis Gasparis (a2) and Pavlos Motakis (a3)

Abstract

Based on a construction method introduced by Bourgain and 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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