Projective generators and resolutions of identity in Banach spaces

Abstract

ABSTRACr. Wc introduce the notion of projective generalor on a given Banach space. Weakly countably detennined asid dual spaces wiih the Radon Nikodym property have projective generators. Ifa Banach space has projective generater, then it adnuits a projective resolution of the identity. When a Banach space asid ita dual both llave a projective generator Usen te s~ncc admits a shrinking resolution of the identity. These results include previous ones of Amir asid Lindesistrauss, John asid Zizer, Gul'ko, VaAak, Tacan, Pablan and Godefroy; asid they shaw how to deal with the general prablern of canstructing projections asid ardering them mt 0 a long sequence in a unified way.