Dunford-Pettis type properties are studied in individual Banach spaces as well as in spaces of operators. Bibasic sequences are used to characterize Banach spaces which fail to have the Dunford-Pettis property. The question of whether a space of operators has a Dunford-Pettis property when the dual of the domain and the codomain have the respective property is studied. The notion of an almost weakly compact operator plays a consistent and important role in this study.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba54-3-6,
author = {Ioana Ghenciu and Paul Lewis},
title = {Almost Weakly Compact Operators},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {54},
year = {2006},
pages = {237-256},
zbl = {1118.46016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba54-3-6}
}
Ioana Ghenciu; Paul Lewis. Almost Weakly Compact Operators. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) pp. 237-256. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba54-3-6/