Higher order spreading models

S. A. Argyros; V. Kanellopoulos; K. Tyros

Fundamenta Mathematicae (2013)

  • Volume: 221, Issue: 1, page 23-68
  • ISSN: 0016-2736

Abstract

top
We introduce higher order spreading models associated to a Banach space X. Their definition is based on ℱ-sequences ( x s ) s 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 ( ξ ( X ) ) ξ < ω . Each ξ ( X ) contains all spreading models generated by ℱ-sequences ( x s ) s with order of ℱ equal to ξ. We also study the fundamental properties of this hierarchy.

How to cite

top

S. A. Argyros, V. Kanellopoulos, and K. Tyros. "Higher order spreading models." Fundamenta Mathematicae 221.1 (2013): 23-68. <http://eudml.org/doc/286676>.

@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 -

NotesEmbed ?

top

You must be logged in to post comments.