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On orthogonally decomposable ordered Banach spaces
Published online by Cambridge University Press: 17 April 2009
Abstract
In a Banach lattice or the hermitian part of a C*-algebra, every element a admits a decomposition a = a+ − a− such that and N(−a) = ‖a−‖, where N is the canonical half-norm of the positive cones. In general ordered Banach spaces, this property is related to the order structure of the duality map and the metric projectability of the positive cones, and it turns out to be equivalent to an “orthogonal” decomposability.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 30 , Issue 3 , December 1984 , pp. 357 - 380
- Copyright
- Copyright © Australian Mathematical Society 1984
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