Vol. 46, No. 1, 1973

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Un théorème du genre “Andô-Edwards” pour les Fréchet ordonnés normaux

Alain Goullet de Rugy

Vol. 46 (1973), No. 1, 155–166
Abstract

Let E be an ordered locally convex topological vector space whose positive cone is normal, closed and generating. It is an important problem to characterize those spaces E, whose topological dual E is a lattice for the dual ordering. It is proved here, with the use of Choquet’s theory of weakly complete cones, that if E is a Fréchet space, Eis lattice if and only if E has the Riesz decomposition property. In fact, a stronger result is proved which is, even in the Banach case, an improvement of the classical Andô’s theorem. An application to the duality of order ideals is given.

Mathematical Subject Classification 2000
Primary: 46A40
Milestones
Received: 16 February 1972
Published: 1 May 1973
Authors
Alain Goullet de Rugy