If every member of a class P of Banach spaces has a projectional resolution of the identity such that certain subspaces arising out of this resolution are also in the class P, then it is proved that every Banach space in P has a strong M-basis. Consequently, every weakly countably determined space, the dual of every Asplund space, every Banach space with an M-basis such that the dual unit ball is weak* angelic and every C(K) space for a Valdivia compact set K , has a strong M-basis.
@article{urn:eudml:doc:41606,
title = {On strong M-bases in Banach spaces with PRI.},
journal = {Collectanea Mathematica},
volume = {51},
year = {2000},
pages = {277-284},
zbl = {0991.46002},
mrnumber = {MR1814330},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41606}
}
Sinha, Deba P. On strong M-bases in Banach spaces with PRI.. Collectanea Mathematica, Tome 51 (2000) pp. 277-284. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41606/