# On super-weakly compact sets and uniformly convexifiable sets

Lixin Cheng; Qingjin Cheng; Bo Wang; Wen Zhang

Studia Mathematica (2010)

- Volume: 199, Issue: 2, page 145-169
- ISSN: 0039-3223

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topLixin 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 -

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