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Une nouvelle définition des cônes biréticulés

Alain Goullet de Rugy (1974)

Annales de l'institut Fourier

On montre que si E est un espace vectoriel réticulé, le cône des formes linéaires positives sur E , muni de la topologie de la convergence simple sur E est un cône biréticulé.Ce résultat conduit à une nouvelle définition des cônes biréticulés, équivalents à la définition initiale, mais d’un usage beaucoup plus souple ; ce résultat est la réponse positive à une hypothèse de G. Choquet.

Uniqueness of unconditional basis of p ( c ) and p ( ) , 0 < p < 1

F. Albiac, C. Leránoz (2002)

Studia Mathematica

We prove that the quasi-Banach spaces p ( c ) and p ( ) (0 < p < 1) have a unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss and Tzafriri have previously proved that the same is true for the respective Banach envelopes ( c ) and ℓ₁(ℓ₂). They used duality techniques which are not available in the non-locally convex case.

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