Higher order spreading models

@article{S2013,
abstract = {We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences $(x_\{s\})_\{s∈ℱ\}$ with ℱ a regular thin family and on plegma families. We show that the higher order spreading models of a Banach space X form an increasing transfinite hierarchy $(ℳ_\{ξ\}(X))_\{ξ<ω₁\}$. Each $ℳ_\{ξ\}(X)$ contains all spreading models generated by ℱ-sequences $(x_\{s\})_\{s∈ℱ\}$ with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy.},
author = {S. A. Argyros, V. Kanellopoulos, K. Tyros},
journal = {Fundamenta Mathematicae},
keywords = {spreading models; Ramsey theory; thin families; plegma families; order of a family},
language = {eng},
number = {1},
pages = {23-68},
title = {Higher order spreading models},
url = {http://eudml.org/doc/286676},
volume = {221},
year = {2013},
}

TY - JOUR
AU - S. A. Argyros
AU - V. Kanellopoulos
AU - K. Tyros
TI - Higher order spreading models
JO - Fundamenta Mathematicae
PY - 2013
VL - 221
IS - 1
SP - 23
EP - 68
AB - We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences $(x_{s})_{s∈ℱ}$ with ℱ a regular thin family and on plegma families. We show that the higher order spreading models of a Banach space X form an increasing transfinite hierarchy $(ℳ_{ξ}(X))_{ξ<ω₁}$. Each $ℳ_{ξ}(X)$ contains all spreading models generated by ℱ-sequences $(x_{s})_{s∈ℱ}$ with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy.
LA - eng
KW - spreading models; Ramsey theory; thin families; plegma families; order of a family
UR - http://eudml.org/doc/286676
ER -