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On orthogonally decomposable ordered Banach spaces

Published online by Cambridge University Press:  17 April 2009

Sadayuki Yamamuro
Sadayuki Yamamuro
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, GPO Box 4, Canberra, ACT 260 I., Australia.
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Abstract

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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.

Information

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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