Given a positive Banach-Saks operator T between two Banach lattices E and F, we give sufficient conditions on E and F in order to ensure that every positive operator dominated by T is Banach-Saks. A counterexample is also given when these conditions are dropped. Moreover, we deduce a characterization of the Banach-Saks property in Banach lattices in terms of disjointness.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm173-2-5,
author = {Julio Flores and C\'esar Ruiz},
title = {Domination by positive Banach-Saks operators},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {185-192},
zbl = {1096.47041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm173-2-5}
}
Julio Flores; César Ruiz. Domination by positive Banach-Saks operators. Studia Mathematica, Tome 173 (2006) pp. 185-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm173-2-5/