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A VERSION OF JAMES' THEOREM FOR NUMERICAL RADIUS

Published online by Cambridge University Press:  01 January 1999

MARÍA D. ACOSTA  and
MANUEL RUIZ GALÁN
MARÍA D. ACOSTA
Affiliation:
Universidad de Granada, Dpto. de Análisis Matemático, Facultad de Ciencias, 18071 Granada, Spain
MANUEL RUIZ GALÁN
Affiliation:
Universidad de Granada, Dpto. de Matemática Aplicada, E. U. Arquitectura Técnica, 18071 Granada, Spain
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Abstract

We prove that if all the rank-one bounded operators on a Banach space X attain their numerical radii, then X must be reflexive, but the converse does not hold. In fact, every reflexive space with basis can be renormed in such a way that there is a rank-one operator not attaining the numerical radius.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 1 , January 1999 , pp. 67 - 74
Copyright
© The London Mathematical Society 1999

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