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On super-weakly compact sets and uniformly convexifiable sets

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Cheng L., Cheng Q., Wang B., Zhang W.

Studia Mathematica

2010

tom 199

nr 2

145-169

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.

Ograniczanie wyników

1 Studia Mathematica

1 Cheng L.

1 Cheng Q.

1 Wang B.

1 Zhang W.

1 2010

Wyniki wyszukiwania

On super-weakly compact sets and uniformly convexifiable sets