It is proved that every positive Banach-Saks operator T: E → F between Banach lattices E and F factors through a Banach lattice with the Banach-Saks property, provided that F has order continuous norm. By means of an example we show that this order continuity condition cannot be removed. In addition, some domination results, in the Dodds-Fremlin sense, are obtained for the class of Banach-Saks operators.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-1-7,
author = {Julio Flores and Pedro Tradacete},
title = {Factorization and domination of positive Banach-Saks operators},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {91-101},
zbl = {1163.47031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-1-7}
}
Julio Flores; Pedro Tradacete. Factorization and domination of positive Banach-Saks operators. Studia Mathematica, Tome 187 (2008) pp. 91-101. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-1-7/