On super-weakly compact sets and uniformly convexifiable sets

• Autorzy: Lixin Cheng , Qingjin Cheng , Bo Wang , Wen Zhang
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 46B50: Compactness in Banach (or normed) spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 199
• Numer: 2
• Strony: 145-169

Daty

wydano

2010

Twórcy

autor

Lixin Cheng

• Department of Mathematics, Xiamen University, Xiamen 361005, China

autor

Qingjin Cheng

• Department of Mathematics, Xiamen University, Xiamen 361005, China

autor

Bo Wang

• Department of Mathematics, Xiamen University, Xiamen 361005, China

autor

Wen Zhang

• Department of Mathematics, Xiamen University, Xiamen 361005, China

Identyfikatory

DOI

10.4064/sm199-2-2