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2015 $p$-variations of vector measures with respect to vector measures and integral representation of operators
O. Blasco , J.M. Calabuig , E.A. Sánchez-Pérez
Banach J. Math. Anal. 9(1): 273-285 (2015). DOI: 10.15352/bjma/09-1-20

Abstract

In this paper we provide two representation theorems for two relevant classes of operators from any $p$-convex order continuous Banach lattice with weak unit into a Banach space: the class of continuous operators and the class of cone absolutely summing operators. We prove that they can be characterized as spaces of vector measures with finite $p$-semivariation and $p$-variation, respectively, with respect to a fixed vector measure. We give in this way a technique for representing operators as integrals with respect to vector measures.

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O. Blasco . J.M. Calabuig . E.A. Sánchez-Pérez. "$p$-variations of vector measures with respect to vector measures and integral representation of operators." Banach J. Math. Anal. 9 (1) 273 - 285, 2015. https://doi.org/10.15352/bjma/09-1-20

Information

Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1337.46034
MathSciNet: MR3296100
Digital Object Identifier: 10.15352/bjma/09-1-20

Subjects:
Primary: 46E30
Secondary: 46G10

Keywords: $p$-semivariation , $p$-variation , operator , vector measures , vector valued integration

Rights: Copyright © 2015 Tusi Mathematical Research Group

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Vol.9 • No. 1 • 2015
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