We generalize some results concerning the classical notion of a spreading model to spreading models of order ξ. Among other results, we prove that the set of ξ-order spreading models of a Banach space X generated by subordinated weakly null ℱ-sequences endowed with the pre-partial order of domination is a semilattice. Moreover, if contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if is uncountable, then it contains an antichain of size continuum.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-2-3,
author = {B\"unyamin Sar\i\ and Konstantinos Tyros},
title = {On the structure of the set of higher order spreading models},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {149-173},
zbl = {1322.46012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-2-3}
}
Bünyamin Sarı; Konstantinos Tyros. On the structure of the set of higher order spreading models. Studia Mathematica, Tome 223 (2014) pp. 149-173. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm223-2-3/