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

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  07 March 2016

Spiros A. Argyros ,
Ioannis Gasparis  and
Pavlos Motakis
Spiros A. Argyros
Affiliation:
National Technical University of Athens, Faculty of Applied Sciences, Department of Mathematics, Zografou Campus, 157 80, Athens, Greece email sargyros@math.ntua.gr
Ioannis Gasparis
Affiliation:
National Technical University of Athens, Faculty of Applied Sciences, Department of Mathematics, Zografou Campus, 157 80, Athens, Greece email ioagaspa@math.ntua.gr
Pavlos Motakis
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, U.S.A. email pavlos@math.tamu.edu

Abstract

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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 $c_{0}$ .

MSC classification

Primary: 46B03: Isomorphic theory (including renorming) of Banach spaces 46B06: Asymptotic theory of Banach spaces 46B07: Local theory of Banach spaces

Information

Type
Research Article
Information
Mathematika , Volume 62 , Issue 3 , 2016 , pp. 685 - 700
Copyright
Copyright © University College London 2016 

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