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Numerical index of Banach spaces and duality

Published online by Cambridge University Press:  12 February 2007

KOSTYANTYN BOYKO
Affiliation:
Faculty of Mechanics and Mathematics, Kharkov National University, pl. Svobody 4, 61077 Kharkov, Ukraine. e-mail: k_boyko@ukr.net, vova1kadets@yahoo.com
VLADIMIR KADETS
Affiliation:
Faculty of Mechanics and Mathematics, Kharkov National University, pl. Svobody 4, 61077 Kharkov, Ukraine. e-mail: k_boyko@ukr.net, vova1kadets@yahoo.com
MIGUEL MARTÍN
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain. e-mail: mmartins@ugr.es
DIRK WERNER
Affiliation:
Department of Mathematics, Freie Universtät Berlin, Arnimallee 2-6, D-14195 Berlin, Germany. e-mail: werner@math.fu-berlin.de

Abstract

We present an example of a Banach space whose numerical index is strictly greater than the numerical index of its dual, giving a negative answer to a question which has been latent since the beginning of the seventies. We also show a particular case in which the numerical index of the space and the one of its dual coincide.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2007

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