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Projetive generators and resolutions of identity in Banach spaces.

J. Orihuela, M. Valdivia (1989)

Revista Matemática de la Universidad Complutense de Madrid

We introduce the notion of projective generator on a given Banach space. Weakly countably determined and dual spaces with the Radon Nikodým property have projective generators. If a Banach space has projective generator, then it admits a projective resolution of the identity. When a Banach space and its dual both have a projective generator then the space admits a shrinking resolution of the identity. These results include previous ones of Amir and Lindenstrauss, John and Zizler, Gul?ko, Vaak, Tacon,...

Properties and applications of Tauberian operators.

Manuel González (1990)

Extracta Mathematicae

Tauberian operators, which appeared in response to a problem in summability [GaW, KW] have found application in several situations: factorization of operators [DFJP], preservation of isomorphic properties of Banach spaces [N, NR], equivalence between the Radon-Nikodym property and the Krein-Milman property [Sch], and generalized Fredholm operators [Ta, Y].This paper is a survey of the main properties and applications of Tauberian operators.

Propriétés géométriques de h p ( 𝔻 , X ) et généralisations

Mohammad Daher (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

Nous montrons que h 2 ( 𝔻 , L 1 ( 𝕋 ) ) admet une norme équivalente L U R , ce qui répond négativement à une question de Dowling, Hu et Smith. Puis nous obtenons une propriété de stabilité des opérateurs de Radon-Nikodym analytique. Motivés par l’identification entre h p ( 𝔻 , X ) et V B p ( 𝕋 , X ) X est un espace de Banach, pour un groupe abélien compact métrisable G , son dual Γ , et Λ 2 Λ 1 Γ , nous prouvons que, si l’espace V B Λ 1 p ( G , X ) / V B Λ 2 p ( G , X ) a la propriété K a d e c - K l e e - β - ω , alors il coincïde avec L Λ 1 p ( G , X ) / L Λ 2 p ( G , X ) , ...

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