On the structure of the set of higher order spreading models

Bünyamin Sarı, and Konstantinos Tyros. "On the structure of the set of higher order spreading models." Studia Mathematica 223.2 (2014): 149-173. <http://eudml.org/doc/285602>.

@article{BünyaminSarı2014,
abstract = {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 $SM_\{ξ\}^\{w\}(X)$ 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 $SM_\{ξ\}^\{w\}(X)$ contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if $SM_\{ξ\}^\{w\}(X)$ is uncountable, then it contains an antichain of size continuum.},
author = {Bünyamin Sarı, Konstantinos Tyros},
journal = {Studia Mathematica},
keywords = {Banach spaces; asymptotic structure; spreading model},
language = {eng},
number = {2},
pages = {149-173},
title = {On the structure of the set of higher order spreading models},
url = {http://eudml.org/doc/285602},
volume = {223},
year = {2014},
}

TY - JOUR
AU - Bünyamin Sarı
AU - Konstantinos Tyros
TI - On the structure of the set of higher order spreading models
JO - Studia Mathematica
PY - 2014
VL - 223
IS - 2
SP - 149
EP - 173
AB - 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 $SM_{ξ}^{w}(X)$ 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 $SM_{ξ}^{w}(X)$ contains an increasing sequence of length ω then it contains an increasing sequence of length ω₁. Finally, if $SM_{ξ}^{w}(X)$ is uncountable, then it contains an antichain of size continuum.
LA - eng
KW - Banach spaces; asymptotic structure; spreading model
UR - http://eudml.org/doc/285602
ER -