Full paper in PDF:
$% J. Orihuela and M. Valdivia, Projective generators and resolutions of identity in Banach spaces, Rev. Mat. Univ. Complut. Madrid 2 (1989), supplementary, 179–199.%$

Projective Generators and Resolutions of Identity in Banach Spaces

José ORIHUELA and Manuel VALDIVIA
Dpto. de Matemáticas
Universidad de Murcia
Sto. Cristo 1
30001 Murcia Spain
Dpto. de Análisis Matemático
Universidad de Valencia
Dr. Moliner 50
46100 Burjassot, Valencia Spain

ABSTRACT

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, Vas  ak, 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.

1980 Mathematics Subject Classification (1985 revision): 46B15, 46B20, 46B22.