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, Fabian, and Godefroy; and they show how to deal with the general problem of constructing projections and ordering them into a long sequence in a unified way.
@article{urn:eudml:doc:43476,
title = {Projetive generators and resolutions of identity in Banach spaces.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {2},
year = {1989},
pages = {179-199},
zbl = {0717.46009},
mrnumber = {MR1057218},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:43476}
}
Orihuela, J.; Valdivia, M. Projetive generators and resolutions of identity in Banach spaces.. Revista Matemática de la Universidad Complutense de Madrid, Tome 2 (1989) pp. 179-199. http://gdmltest.u-ga.fr/item/urn:eudml:doc:43476/