On super-weakly compact sets and uniformly convexifiable sets

Lixin Cheng, et al. "On super-weakly compact sets and uniformly convexifiable sets." Studia Mathematica 199.2 (2010): 145-169. <http://eudml.org/doc/285450>.

@article{LixinCheng2010,
abstract = {This paper mainly concerns the topological nature of uniformly convexifiable sets in general Banach spaces: A sufficient and necessary condition for a bounded closed convex set C of a Banach space X to be uniformly convexifiable (i.e. there exists an equivalent norm on X which is uniformly convex on C) is that the set C is super-weakly compact, which is defined using a generalization of finite representability. The proofs use appropriate versions of classical theorems, such as James' finite tree theorem, Enflo's renorming technique, Grothendieck's lemma and the Davis-Figiel-Johnson-Pełczyński lemma.},
author = {Lixin Cheng, Qingjin Cheng, Bo Wang, Wen Zhang},
journal = {Studia Mathematica},
keywords = {finite representability; weakly compact sets; uniformly convexifiable set; Banach space},
language = {eng},
number = {2},
pages = {145-169},
title = {On super-weakly compact sets and uniformly convexifiable sets},
url = {http://eudml.org/doc/285450},
volume = {199},
year = {2010},
}

TY - JOUR
AU - Lixin Cheng
AU - Qingjin Cheng
AU - Bo Wang
AU - Wen Zhang
TI - On super-weakly compact sets and uniformly convexifiable sets
JO - Studia Mathematica
PY - 2010
VL - 199
IS - 2
SP - 145
EP - 169
AB - This paper mainly concerns the topological nature of uniformly convexifiable sets in general Banach spaces: A sufficient and necessary condition for a bounded closed convex set C of a Banach space X to be uniformly convexifiable (i.e. there exists an equivalent norm on X which is uniformly convex on C) is that the set C is super-weakly compact, which is defined using a generalization of finite representability. The proofs use appropriate versions of classical theorems, such as James' finite tree theorem, Enflo's renorming technique, Grothendieck's lemma and the Davis-Figiel-Johnson-Pełczyński lemma.
LA - eng
KW - finite representability; weakly compact sets; uniformly convexifiable set; Banach space
UR - http://eudml.org/doc/285450
ER -