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.
@article{bwmeta1.element.bwnjournal-article-smv125i3p255bwm,
author = {L. Rodr\'\i guez-Piazza and M. Romero-Moreno},
title = {Conical measures and properties of a vector measure determined by its range},
journal = {Studia Mathematica},
volume = {122},
year = {1997},
pages = {255-270},
zbl = {0910.46034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv125i3p255bwm}
}
Rodríguez-Piazza, L.; Romero-Moreno, M. Conical measures and properties of a vector measure determined by its range. Studia Mathematica, Tome 122 (1997) pp. 255-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv125i3p255bwm/
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