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

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 $c_0$.

15 pages

Cited by in corpus (4)

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