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Revista Matemática Complutense

, Volume 30, Issue 2, pp 417–426 | Cite as

Nice operators into \(L_1\)-preduals

  • Ana M. Cabrera-Serrano
  • Juan F. Mena-JuradoEmail author
Article
  • 158 Downloads

Abstract

A Banach space X is said to be “nice” if every extreme operator from any Banach space into X is a nice operator (that is, its adjoint preserves extreme points). We prove that a nice \(L_1\)-predual space is isometrically isomorphic to \(c_0(I)\) for some set I. In fact, by using the structure topology, we get a more general result which allows us to conclude that there exist extreme non-nice operators into certain spaces of continuous affine functions which are not \(L_1\)-preduals.

Keywords

Extreme operator Nice operator \(L_1\)-predual Structure topology 

Mathematics Subject Classification

46B20 46B04 

Notes

Acknowledgements

Thanks are due to the referees for several useful suggestions and remarks that improved the final version of the paper.

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Copyright information

© Universidad Complutense de Madrid 2016

Authors and Affiliations

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

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