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