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Projetive generators and resolutions of identity in Banach spaces.

J. OrihuelaM. 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,...

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