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ArticleOriginal scientific text

Title

Numerical index of vector-valued function spaces

Authors 1, 1

Affiliations

  1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Abstract

We show that the numerical index of a c0-, l1-, or l∞-sum of Banach spaces is the infimum of the numerical indices of the summands. Moreover, we prove that the spaces C(K,X) and L1(μ,X) (K any compact Hausdorff space, μ any positive measure) have the same numerical index as the Banach space X. We also observe that these spaces have the so-called Daugavet property whenever X has the Daugavet property.

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Studia Mathematica
2000/142/3
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Pages:
269-280
Main language of publication
English
Received
1999-10-18
Accepted
2000-06-19
Published
2000
Exact and natural sciences