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REAL BANACH SPACES WITH NUMERICAL INDEX 1

Published online by Cambridge University Press:  01 March 1999

GINÉS LÓPEZ ,
MIGUEL MARTÍN  and
RAFAEL PAYÁ
GINÉS LÓPEZ
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
MIGUEL MARTÍN
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
RAFAEL PAYÁ
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
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Abstract

We show that an infinite-dimensional real Banach space with numerical index 1 satisfying the Radon–Nikodym property contains l1. It follows that a reflexive or quasi-reflexive real Banach space cannot be re-normed to have numerical index 1, unless it is finite-dimensional.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 2 , March 1999 , pp. 207 - 212
Copyright
© The London Mathematical Society 1999

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