Estimation of the Szlenk index of Banach spaces via Schreier spaces

Ryan Causey. "Estimation of the Szlenk index of Banach spaces via Schreier spaces." Studia Mathematica 216.2 (2013): 149-178. <http://eudml.org/doc/285547>.

@article{RyanCausey2013,
abstract = {For each ordinal α < ω₁, we prove the existence of a Banach space with a basis and Szlenk index $ω^\{α+1\}$ which is universal for the class of separable Banach spaces with Szlenk index not exceeding $ω^\{α\}$. Our proof involves developing a characterization of which Banach spaces embed into spaces with an FDD with upper Schreier space estimates.},
author = {Ryan Causey},
journal = {Studia Mathematica},
keywords = {szlenk index; universality; embedding in spaces with finitedimensional decompositions; Schreier spaces},
language = {eng},
number = {2},
pages = {149-178},
title = {Estimation of the Szlenk index of Banach spaces via Schreier spaces},
url = {http://eudml.org/doc/285547},
volume = {216},
year = {2013},
}

TY - JOUR
AU - Ryan Causey
TI - Estimation of the Szlenk index of Banach spaces via Schreier spaces
JO - Studia Mathematica
PY - 2013
VL - 216
IS - 2
SP - 149
EP - 178
AB - For each ordinal α < ω₁, we prove the existence of a Banach space with a basis and Szlenk index $ω^{α+1}$ which is universal for the class of separable Banach spaces with Szlenk index not exceeding $ω^{α}$. Our proof involves developing a characterization of which Banach spaces embed into spaces with an FDD with upper Schreier space estimates.
LA - eng
KW - szlenk index; universality; embedding in spaces with finitedimensional decompositions; Schreier spaces
UR - http://eudml.org/doc/285547
ER -