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- Title
Positive Representations of L <sup>1</sup> of a Vector Measure.
- Authors
Ricardo del Campo; Enrique Sánchez-Pérez
- Abstract
Abstract 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 L1(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.
- Subjects
VECTOR analysis; BANACH lattices; OPERATOR spaces; MATHEMATICAL analysis
- Publication
Positivity, 2007, Vol 11, Issue 3, p449
- ISSN
1385-1292
- Publication type
Article
- DOI
10.1007/s11117-007-2075-9