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

Normed linear spaces and Banach spaces; Banach lattices

Spiros A. Argyros, Ioannis Gasparis, Pavlos Motakis
Journal: Mathematika / Volume 62 / Issue 3 / 2016
Published online by Cambridge University Press: 07 March 2016, pp. 685-700
Print publication: 2016
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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 $c_{0}$.