Geodesic
Conical measures and properties of a vector measure determined by its range
Studia Mathematica, Tome 125 (1997) no. 3, pp. 255-270

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-125-3-255-270
Keywords: vector measures, range, conical measures, operator ideal norms, Pettis integral

L. Rodríguez-Piazza 1 ;  1

1 
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L. Rodríguez-Piazza;  . Conical measures and properties of a vector measure determined by its range. Studia Mathematica, Tome 125 (1997) no. 3, pp. 255-270. doi: 10.4064/sm-125-3-255-270

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