Projetive generators and resolutions of identity in Banach spaces.

Orihuela, J., and Valdivia, M.. "Projetive generators and resolutions of identity in Banach spaces.." Revista Matemática de la Universidad Complutense de Madrid 2.SUPL. (1989): 179-199. <http://eudml.org/doc/43476>.

@article{Orihuela1989,
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, 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.},
author = {Orihuela, J., Valdivia, M.},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Espacios de Banach; Generadores; Weakly countably determined and dual spaces with the Radon-Nikodym property have projective generators; projective resolution of the identity; shrinking resolution of the identity; constructing projections and ordering them into a long sequence},
language = {eng},
number = {SUPL.},
pages = {179-199},
title = {Projetive generators and resolutions of identity in Banach spaces.},
url = {http://eudml.org/doc/43476},
volume = {2},
year = {1989},
}

TY - JOUR
AU - Orihuela, J.
AU - Valdivia, M.
TI - Projetive generators and resolutions of identity in Banach spaces.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1989
VL - 2
IS - SUPL.
SP - 179
EP - 199
AB - 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.
LA - eng
KW - Espacios de Banach; Generadores; Weakly countably determined and dual spaces with the Radon-Nikodym property have projective generators; projective resolution of the identity; shrinking resolution of the identity; constructing projections and ordering them into a long sequence
UR - http://eudml.org/doc/43476
ER -