Banach spaces of bounded Szlenk index

E. Odell, Th. Schlumprecht, and A. Zsák. "Banach spaces of bounded Szlenk index." Studia Mathematica 183.1 (2007): 63-97. <http://eudml.org/doc/284580>.

@article{E2007,
abstract = {For a countable ordinal α we denote by $_\{α\}$ the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by α. We show that each $_\{α\}$ admits a separable, reflexive universal space. We also show that spaces in the class $_\{ω^\{α·ω\}\}$ embed into spaces of the same class with a basis. As a consequence we deduce that each $_\{α\}$ is analytic in the Effros-Borel structure of subspaces of C[0,1].},
author = {E. Odell, Th. Schlumprecht, A. Zsák},
journal = {Studia Mathematica},
keywords = {Szlenk index; universal space; embedding into FDDs; Effros-Borel structure; analytic classes},
language = {eng},
number = {1},
pages = {63-97},
title = {Banach spaces of bounded Szlenk index},
url = {http://eudml.org/doc/284580},
volume = {183},
year = {2007},
}

TY - JOUR
AU - E. Odell
AU - Th. Schlumprecht
AU - A. Zsák
TI - Banach spaces of bounded Szlenk index
JO - Studia Mathematica
PY - 2007
VL - 183
IS - 1
SP - 63
EP - 97
AB - For a countable ordinal α we denote by $_{α}$ the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by α. We show that each $_{α}$ admits a separable, reflexive universal space. We also show that spaces in the class $_{ω^{α·ω}}$ embed into spaces of the same class with a basis. As a consequence we deduce that each $_{α}$ is analytic in the Effros-Borel structure of subspaces of C[0,1].
LA - eng
KW - Szlenk index; universal space; embedding into FDDs; Effros-Borel structure; analytic classes
UR - http://eudml.org/doc/284580
ER -