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

L. Rodríguez-Piazza; M. Romero-Moreno

Studia Mathematica (1997)

- Volume: 125, Issue: 3, page 255-270
- ISSN: 0039-3223

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topRodríguez-Piazza, L., and Romero-Moreno, M.. "Conical measures and properties of a vector measure determined by its range." Studia Mathematica 125.3 (1997): 255-270. <http://eudml.org/doc/216437>.

@article{Rodríguez1997,

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.},

author = {Rodríguez-Piazza, L., Romero-Moreno, M.},

journal = {Studia Mathematica},

keywords = {vector measures; range; conical measures; operator ideal norms; Pettis integral; operator ideal; associated Kluvánek conical measure; range of a vector measure; total variation; -finiteness; Bochner derivability; -summing; -nuclear norm; integration operator; Pettis derivability},

language = {eng},

number = {3},

pages = {255-270},

title = {Conical measures and properties of a vector measure determined by its range},

url = {http://eudml.org/doc/216437},

volume = {125},

year = {1997},

}

TY - JOUR

AU - Rodríguez-Piazza, L.

AU - Romero-Moreno, M.

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

JO - Studia Mathematica

PY - 1997

VL - 125

IS - 3

SP - 255

EP - 270

AB - 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.

LA - eng

KW - vector measures; range; conical measures; operator ideal norms; Pettis integral; operator ideal; associated Kluvánek conical measure; range of a vector measure; total variation; -finiteness; Bochner derivability; -summing; -nuclear norm; integration operator; Pettis derivability

UR - http://eudml.org/doc/216437

ER -

## References

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- [R1] L. Rodríguez-Piazza, The range of a vector measure determines its total variation, Proc. Amer. Math. Soc. 111 (1991), 205-214. Zbl0727.28005
- [R2] L. Rodríguez-Piazza, Derivability, variation and range of a vector measure, Studia Math. 112 (1995), 165-187.
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- [Th] E. Thomas, Integral representations in convex cones, Groningen University Report ZW-7703 (1977).

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