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ArticleOriginal scientific text

Title

Conical measures and properties of a vector measure determined by its range

Authors 1, 1

Affiliations

  1. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain

Abstract

We characterize some properties of a vector measure in terms of its associated Kluvánek conical measure. These characterizations are used to prove that the range of a vector measure determines these properties. So we give new proofs of the fact that the range determines the total variation, the σ-finiteness of the variation and the Bochner derivability, and we show that it also determines the (p,q)-summing and p-nuclear norm of the integration operator. Finally, we show that Pettis derivability is not determined by the range and study when every measure having the same range of a given measure has a Pettis derivative.

Keywords

ENG
vector measures, range, conical measures, operator ideal norms, Pettis integral

Bibliography

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Studia Mathematica
1997/125/3
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Pages:
255-270
Main language of publication
English
Received
1996-11-06
Published
1997
Exact and natural sciences