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Antonio Fernández, F. Mayoral, F. Naranjo, C. Saez, E. Sánchez-Pérez (2007)
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We characterize the vector measures n on a Banach lattice such that the map $$\|\int|\cdot|dn \|$$ provides a quasi-norm which is equivalent to the canonical norm $$\|\cdot\|_{n}$$ of the space L 1(n) of integrable functions as an specific type of transformations of positive vector measures that we call cone-open transformations. We also prove that a vector measure m on a Banach space X constructed as a cone-open transformation of a positive vector measure can be considered in some sense as a positive vector measure by defining a new order on X.
Positivity – Springer Journals
Published: Jan 1, 2007
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