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Published online by Cambridge University Press:  07 March 2016

Spiros A. Argyros
National Technical University of Athens, Faculty of Applied Sciences, Department of Mathematics, Zografou Campus, 157 80, Athens, Greece email
Ioannis Gasparis
National Technical University of Athens, Faculty of Applied Sciences, Department of Mathematics, Zografou Campus, 157 80, Athens, Greece email
Pavlos Motakis
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, U.S.A. email
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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 $c_{0}$.

Research Article
Copyright © University College London 2016 

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