Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-13T11:32:39.711Z Has data issue: false hasContentIssue false
  • English
  • Français

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 ([email protected]; [email protected])
Armando R. Villena
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain ([email protected]; [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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