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NUMERICAL INDEX AND THE DAUGAVET PROPERTY FOR $L_\infty(\mu,X)$

Published online by Cambridge University Press:  04 July 2003

Miguel Martín  and
Armando R. Villena
Miguel Martín
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain (mmartins@ugr.es; avillena@ugr.es)
Armando R. Villena
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain (mmartins@ugr.es; avillena@ugr.es)
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Abstract

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We prove that the space $L_\infty(\mu,X)$ has the same numerical index as the Banach space $X$ for every $\sigma$-finite measure $\mu$. We also show that $L_\infty(\mu,X)$ has the Daugavet property if and only if $X$ has or $\mu$ is atomless.

AMS 2000 Mathematics subject classification: Primary 46B20; 47A12

Keywords

Daugavet propertynumerical indexnumerical radius
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 2 , June 2003 , pp. 415 - 420
Copyright
Copyright © Edinburgh Mathematical Society 2003