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

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Rodríguez-Piazza L., Romero-Moreno M. C.

Studia Mathematica

1997

tom 125

nr 3

255-270

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.

Ograniczanie wyników

1 Studia Mathematica

1 Rodríguez-Piazza L.

1 Romero-Moreno M. C.

1 1997

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