On super-weakly compact sets and uniformly convexifiable sets

Tom 199 / 2010

Lixin Cheng, Qingjin Cheng, Bo Wang, Wen Zhang Studia Mathematica 199 (2010), 145-169 MSC: Primary 46B20, 46B03, 46B50. DOI: 10.4064/sm199-2-2

Streszczenie

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.

Autorzy

  • Lixin ChengDepartment of Mathematics
    Xiamen University
    Xiamen 361005, China
    e-mail
  • Qingjin ChengDepartment of Mathematics
    Xiamen University
    Xiamen 361005, China
    e-mail
  • Bo WangDepartment of Mathematics
    Xiamen University
    Xiamen 361005, China
    e-mail
  • Wen ZhangDepartment of Mathematics
    Xiamen University
    Xiamen 361005, China
    e-mail

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