This paper studies the Banach-Saks property in rearrangement invariant spaces on the positive half-line. A principal result of the paper shows that a separable rearrangement invariant space E with the Fatou property has the Banach-Saks property if and only if E has the Banach-Saks property for disjointly supported sequences. We show further that for Orlicz and Lorentz spaces, the Banach-Saks property is equivalent to separability although the separable parts of some Marcinkiewicz spaces fail the Banach-Saks property.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-3-6,
author = {P. G. Dodds and E. M. Semenov and F. A. Sukochev},
title = {The Banach-Saks property in rearrangement invariant spaces},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {263-294},
zbl = {1057.46016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-3-6}
}
P. G. Dodds; E. M. Semenov; F. A. Sukochev. The Banach-Saks property in rearrangement invariant spaces. Studia Mathematica, Tome 162 (2004) pp. 263-294. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-3-6/