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Nice Operators into G-Spaces

Article

Abstract

G-spaces are a class of \(L_1\)-preduals introduced by Grothendieck. We prove that if every extreme operator from any Banach space into a G-space, X, is a nice operator (that is, its adjoint preserves extreme points), then X is isometrically isomorphic to \(c_0(I)\) for some set I. One of the main points in the proof is a characterization of spaces of type \(c_0(I)\) by means of the structure topology on the extreme points of the dual space.

Keywords

Banach space Extreme operator Nice operator G-space  Structure topology 

Mathematics Subject Classification

46B20 46B04 

Notes

Acknowledgments

This study was supported by Spanish MICINN and FEDER Project No. MTM2012-31755 and by Junta de Andalucía and FEDER Grants FQM-185 and FQM-3737.

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Copyright information

© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2015

Authors and Affiliations

  1. 1.Departamento de Análisis Matemático, Facultad de CienciasUniversidad de GranadaGranadaSpain

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