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Extensions uniformes des formes linéaires positives

Hicham Fakhoury (1973)

Annales de l'institut Fourier

Soit M un sous-espace fermé d’un espace de Banach ordonné V  ; ce travail propose des conditions nécessaires et suffisantes pour qu’il existe a 1 , tel que toute forme linéaire f positive et continue sur M admette une extension linéaire f ˜ positive et continue sur V , vérifiant f ˜ a f . On termine par l’exemple d’un couple ( M , V ) ne possédant pas la propriété précédente bien que toute forme linéaire positive continue sur M se prolonge en une forme linéaire du même type en V .

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